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How to Study Coordinate Geometry for JEE | Complete PYQ Analysis (JEE Main 2024–2026 & JEE Advanced 2015–2026)

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PYQ Analysis 2024–2026

How to Study Coordinate Geometry for JEE | Complete PYQ Analysis (JEE Main 2024–2026 & JEE Advanced 2015–2026)

By Team JEE Prep Master · Updated October 2026 · ~27 min read

If you are wondering how to study Coordinate Geometry for JEE, start with one number. JEE Main asked 218 questions from Straight Lines, Circles, Parabola, Ellipse and Hyperbola across 2024, 2025 and 2026. That is about one in every seven Maths questions, more than any other single area of the syllabus. JEE Advanced asked 60 questions from the same five parts between 2015 and 2026, and it asked them in every one of those twelve years. This guide breaks all of them down, based on the papers conducted by the National Testing Agency (jeemain.nta.ac.in) for JEE Main and the JEE Advanced papers from 2015 to 2026.

We went through every one of those questions and tagged it twice: once by the part it comes from, and once by the kind of work it needs. The kinds are triangle and area geometry, focus and eccentricity properties of conics, intersections and chords, tangents and normals, locus, distances and images, and finding the equation of a line or circle. The tables below show where the marks come from, and the rest of the guide shows how to win them.

The single most useful finding is a split between the two exams. In JEE Main, tangents and normals gave only 22 of 218 questions; the marks came from triangle geometry and the standard properties of each conic. In JEE Advanced, tangents, normals and common tangents appear in well over half of the 60 questions. One chapter, two very different exams, and your preparation should reflect both.

1. Why Coordinate Geometry Is High Priority for JEE

It is the biggest block of marks in JEE Main Maths. JEE Main had 75 questions from these five parts in 2024, 72 in 2025 and 71 in 2026. That is about 12.5%, 15.2% and 15.0% of all Maths questions in those years, or roughly three to four questions in every paper. No other Maths area comes close.

JEE Advanced has never skipped it. Between 2015 and 2026, Advanced asked between 3 and 9 questions from Coordinate Geometry every year, 60 in total. Parabola alone gave 18 of them and Circles gave 16.

The questions are predictable. In JEE Main, 60 of the 218 questions were about the focus, directrix, eccentricity and latus rectum of a conic, and 46 were triangle or area questions. Two kinds of question, almost half the chapter. Very few chapters are this pattern-driven.

It rewards speed. Most Main questions are two or three clean steps once you know the standard result. Students who know the parametric forms and the T = S1 family of results finish these in under two minutes and save time for the harder chapters. It also links directly to 3D Geometry, which uses the same distance, image and family-of-lines ideas in space.

"Coordinate Geometry is a chapter of standard results. The student who has the twenty key formulas ready in their head finishes the question while others are still drawing the figure. Learn the results by heart, then practise until you never need to derive them in the exam." — AKS Yadav Sir, Maths HOD (IIT BHU, AIR 1 FTRE 2009, Ex-Faculty Allen Delhi)

Real result · JEE 2026

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Coordinate Geometry is about one in every seven JEE Main Maths questions. Start where the chapter starts: learn Straight Lines and triangle geometry 1-on-1 with an IITian Maths HOD.

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2. JEE Main PYQ Analysis 2024–2026

Any plan for how to study Coordinate Geometry for JEE should start from the papers. Here is how many questions JEE Main asked from each part in each of the last three years.

Part202420252026Total
Straight Lines24181456
Circles20101545
Parabola12171443
Ellipse8181541
Hyperbola1191333
Total757271218
MCQ + Numerical52 + 2358 + 1459 + 12169 + 49
Share of Maths Qs12.5%15.2%15.0%—

Two trends stand out. Straight Lines is shrinking, from 24 questions in 2024 to 14 in 2026. The conics are growing: Parabola, Ellipse and Hyperbola together gave 31 questions in 2024, 44 in 2025 and 42 in 2026. If your plan still spends most of its time on lines and circles, it is planning for an older exam.

And here are the same 218 questions sorted by the kind of work they need.

Question typeLinesCirclesParabolaEllipseHyperbolaTotal
Focus, directrix, eccentricity, latus rectum and standard properties of conics——14212560
Triangles, quadrilaterals and areas (centres, vertices, area of a triangle)25555646
Intersections, chords, families and two-circle problems811124136
Tangents, normals, chords with a given midpoint—786122
Locus6445019
Distances, images and foot of perpendicular125———17
Finding a line or circle, angle bisectors, standard properties512———17
Not classified*010001
Total5645434133218

*The archived text of one 2026 Circles question did not render fully, so we could not tell what it asked. It is counted in the totals only. Questions that need two kinds of work are counted under the one that finishes them. A dash means the type does not apply to that part (for example, Straight Lines has no focus).

The message of this table is simple. Focal properties of conics (60) and triangle geometry (46) gave 106 of the 218 questions, almost half. Add intersections and chords and you have 142 of 218, about two in every three. Tangents and normals, the topic most students spend the most time on, gave just 22.

5 key patterns from recent JEE Main papers

Pattern 1: Triangle geometry with lines. Straight Lines in JEE Main is mostly triangles. 2026 asked for an equilateral triangle with its orthocentre at the origin, the area of a triangle whose vertices lie on parallel lines, the incentre of a triangle from the midpoints of its sides, and a rhombus with opposite vertices A(1, 2) and C(−3, 6). Know the centroid, incentre, circumcentre and orthocentre formulas, and the fact that in an equilateral triangle they all coincide.

Pattern 2: Focal properties of every conic. 2025 gave a hyperbola with foci (1, 14) and (1, −12) passing through a given point, and asked for its latus rectum. 2024 and 2026 both asked about a hyperbola confocal with a given ellipse. 2025 and 2026 asked for an ellipse's eccentricity defined through the maximum or minimum of a function. Each is a direct use of c2 = a2 ± b2, e = c/a and latus rectum = 2b2/a.

Pattern 3: Chords with a given midpoint. Ellipse chords bisected at a given point appeared four times in 2025 and once in 2024. The 2026 Circles paper asked about chords from (1, 2) bisected by the y-axis. All of them use the same result, T = S1, which gives the chord in one line.

Pattern 4: Focal chords and chords through a fixed point. 2024 gave a focal chord of y2 = 12x of length 15. 2025 gave a focal chord through P(4, 4√3) and asked for the area of a quadrilateral. 2026 asked about a chord of a parabola that subtends a right angle at the vertex. The parametric form (at2, 2at) with t1t2 = −1 for focal chords and t1t2 = −4 for right-angle chords solves each of them.

Pattern 5: Images and families. 2026 asked for the image of x2 = 4y in the line x − y = 1, 2025 asked for the image of a circle in a line, and several 2024 numericals were about a ray of light reflected from a line. The family of lines x(3λ + 1) + y(7λ + 2) = 17λ + 5 (2025) passes through a fixed point, which the question needed you to find. Reflection and family-of-lines results carry across all five parts.

3. JEE Advanced PYQ Pattern 2015–2026

This is the 12-year view that most guides skip. JEE Advanced asked Coordinate Geometry in every year from 2015 to 2026.

YearQsWhat was asked
20265A circle through points found from tangent slopes to a parabola and an ellipse · perpendicular tangents to a parabola and the distance to its focus · the angle between tangents to two ellipses at a common point (numerical) · a match-the-columns on circle, parabola, ellipse and hyperbola · the intersection of a confocal ellipse and hyperbola (numerical)
20253Locus of the intersection of two line pairs, with a tangent · locus of midpoints of parabola chords that cut off a fixed area (multi-correct) · points on two ellipses and a circle, a segment length (multi-correct)
20244A circle touching y2 = x (match) · tangents to a parabola at two points (multi-correct) · a normal of slope 1/√6 (numerical) · tangents from a point to an ellipse and an area
20234A regular octagon on a circle of radius 2, the maximum product of distances (numerical) · common tangents of two circles, the midpoint line meeting the x-axis (numerical) · a normal to a parabola with area of triangle PQS = 120 · common tangents to an ellipse and a parabola (multi-correct)
20225A circle touching two sides of a triangle and its circumcircle (numerical) · n equal circles touching a larger circle (multi-correct) · tangents from a point to y2 = 4x (multi-correct) · a tangent to an ellipse and a triangle area · a hyperbola with a line parallel to a tangent (numerical)
20219Two numericals on the locus C of points with a fixed product of distances from two lines · two questions on circles Cn and Dn inside a disc, combined with a geometric progression · a circumcircle from the orthocentre (1, 1) · two numericals on the largest circle inside a parabolic region · tangents to y2 = 8x from a point (multi-correct) · maximum distance in an ellipse (numerical)
20203A chord on 2x + 4y = 5 and the circumcentre of OPQ (numerical) · a latus-rectum end, an ellipse and perpendicular tangents, find e · a hyperbola whose normal has equal intercepts (multi-correct)
20195The midpoint of a chord cut by y = mx + 1 · a reflection and a common tangent (numerical) · two match-the-columns on circles and x2 = 8y · nested ellipses and rectangles (multi-correct)
20185Chords of x2 + y2 = 4 through (1, 1) and the intersection of their tangents · a tangent to x2 + y2 = 4 and the locus of a midpoint · common tangents of a circle and a parabola, with an ellipse (multi-correct) · a hyperbola whose conjugate axis subtends 60° (match) · a line, circles and a locus (multi-correct)
20176The tangent y = x + 8 at (8, 16) (match) · the chord 2x + y = p of y2 = 16x and its midpoint (multi-correct) · a circle meeting the axes at exactly three points (numerical) · two match-the-columns on tangents to a suitable conic · the tangent 2x − y + 1 = 0 to a hyperbola and right-triangle sides (multi-correct)
20165The locus of E with RS a diameter (multi-correct) · the point of a parabola nearest to a circle's centre (multi-correct) · x2 + y2 = 3 meeting a parabola, with a tangent touching two circles (multi-correct) · two questions on an ellipse and a parabola: an orthocentre and an area ratio
20156A circle on a parabola chord PQ through the vertex (multi-correct) · parabolas with an ellipse's foci and tangent slopes (numerical) · normals at the latus-rectum ends tangent to a circle (numerical) · the mirror image of y2 = 4x (numerical) · two ellipses with a common tangent and a circle (multi-correct) · x2 − y2 = 1 and a circle with a common tangent, a centroid (multi-correct)
Total60Straight Lines 3 · Circles 16 · Parabola 18 · Ellipse 13 · Hyperbola 10

Questions are counted under the chapter the archive files them in. Several questions filed under Ellipse or Hyperbola are mostly about circles, and many combine two conics; they are counted once each.

This table changes how to study Coordinate Geometry for JEE Advanced, because Advanced is a different exam for this chapter. Tangents, normals and common tangents appear in well over half of the 60 questions, and most questions combine two curves: a circle and a parabola, an ellipse and a parabola, or an ellipse and a hyperbola. Straight Lines on its own almost disappears (3 questions in 12 years), but lines are inside every other question as tangents, chords and normals. Multi-correct and match-the-columns formats are common, so you need to be sure of every property, not just the one you used.

4. Complete Sub-topic Breakdown

The smartest way to decide how to study Coordinate Geometry for JEE is to match your time to each part. Use the time column in your mock tests: if you are consistently slower than the target, that part needs more practice, not more reading.

PartMain Qs (2024–26)Advanced Qs (2015–26)DifficultyTarget time
Straight Lines563Easy–Medium90 s–2 min
Circles4516Medium2–3 min
Parabola4318Medium2–3 min
Ellipse4113Medium2–3 min
Hyperbola3310Medium2 min

Difficulty and target time are our faculty's guidance for exam practice, not exam data.

Straight Lines covers distance and section formulas, the forms of a line, the angle between lines, distance of a point from a line, the image of a point, angle bisectors, families of lines and pair of lines. In JEE Main it is mostly applied to triangles: 25 of its 56 questions were triangle or quadrilateral geometry.

Circles covers the equation of a circle, the position of a point or line, tangents and normals, chord of contact, chord with a given midpoint, family of circles, and two circles (common chord, common tangents, orthogonality). In JEE Main, finding a circle from conditions (12) and intersections or two-circle problems (11) lead.

Parabola covers the four standard forms, focus, directrix and latus rectum, the parametric form, focal chords, tangents and normals. Its 43 Main questions are spread across focal properties (14), chords and intersections (12), tangents and normals (8), areas (5) and locus (4).

Ellipse covers the standard form, eccentricity, foci, directrices, latus rectum, focal distances, the auxiliary circle and the parametric form. Half its Main questions (21 of 41) were focal properties.

Hyperbola covers the standard and conjugate forms, eccentricity, foci, latus rectum, asymptotes and the rectangular hyperbola. It is the most predictable part: 25 of its 33 Main questions were focal properties, and most of the rest were areas.

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5. Common Mistakes in Coordinate Geometry

Knowing how to study Coordinate Geometry for JEE also means knowing what not to do. These are the mistakes we see most often when students solve this chapter's PYQs.

Mistake 1: Mixing up c2 = a2 − b2 and c2 = a2 + b2. For an ellipse b2 = a2(1 − e2); for a hyperbola b2 = a2(e2 − 1). Confocal questions put both in one problem, which is exactly where students swap them. Fix: write the relation for each curve on its own line before you start.
Mistake 2: Assuming the major axis is along the x-axis. If b > a in x2/a2 + y2/b2 = 1, the major axis is vertical and the foci are (0, ±be). Fix: compare the two denominators first. The larger one is the semi-major axis squared, whichever variable it sits under.
Mistake 3: Using the standard-form results on a shifted curve. For y2 − 4y = 8x, the focus is not (2, 0). Fix: complete the square, shift the origin to the vertex or centre, use the standard result, then shift back.
Mistake 4: Using T = 0 for a chord when the point is not on the curve. T = 0 is the tangent at a point on the curve and the chord of contact from a point outside. A chord bisected at a point needs T = S1. Fix: check where the given point lies (S1 < 0, = 0 or > 0) before choosing the equation.
Mistake 5: Forgetting both answers. Angle bisectors, tangents of a given slope, lines at a given distance and points dividing a segment externally all come in pairs. Single-correct questions often list one of them; multi-correct questions list both. Fix: keep the ± sign until the very last step.
Mistake 6: Wrong condition for "no triangle" or "concurrent". Three lines fail to form a triangle if any two are parallel or if all three are concurrent. Students check only one of these. Fix: test both: equal slopes for each pair, and the determinant of coefficients for concurrency.
Mistake 7: Drawing a figure to scale and trusting it. Many locus and maximum-distance questions have an answer that looks wrong on a rough sketch. Fix: use the figure only to set up the algebra. Take the answer from the algebra.
Mistake 8: Using the circle's tangent condition for a conic. For a circle, c2 = r2(1 + m2); for an ellipse, c2 = a2m2 + b2; for a hyperbola, c2 = a2m2 − b2; for y2 = 4ax, c = a/m. Fix: keep these four in one row of your formula sheet and say the curve's name before writing the condition.

6. Important Formulas by Sub-topic

Keep this table open while you practise. Most of the chapter runs on these results, which is why learning how to study Coordinate Geometry for JEE is mostly about knowing them cold and choosing the right one quickly.

PartFormula / result
PointsSection formula ((mx2 + nx1)/(m + n), …) · area = ½|x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|
Triangle centresCentroid ((x1 + x2 + x3)/3, …) · incentre ((ax1 + bx2 + cx3)/(a + b + c), …) · O, G, H collinear with HG : GO = 2 : 1
LinesDistance of (x1, y1) from ax + by + c = 0 is |ax1 + by1 + c|/√(a2 + b2) · between parallel lines |c1 − c2|/√(a2 + b2) · tan θ = |(m1 − m2)/(1 + m1m2)|
Image and foot(x − x1)/a = (y − y1)/b = −2(ax1 + by1 + c)/(a2 + b2) for the image (−1 instead of −2 for the foot)
Families and bisectorsL1 + λL2 = 0 passes through the intersection of L1, L2 · bisectors (a1x + b1y + c1)/√(a12 + b12) = ±(a2x + b2y + c2)/√(a22 + b22)
Circlex2 + y2 + 2gx + 2fy + c = 0 · centre (−g, −f) · r = √(g2 + f2 − c) · diameter form (x − x1)(x − x2) + (y − y1)(y − y2) = 0
Chord results (all conics)Tangent at a point on the curve: T = 0 · chord of contact: T = 0 · chord bisected at (x1, y1): T = S1 · pair of tangents: SS1 = T2
Two circlesd > r1 + r2: 4 common tangents · d = r1 + r2: 3 · |r1 − r2| < d < r1 + r2: 2 · common chord S1 − S2 = 0 · orthogonal: 2g1g2 + 2f1f2 = c1 + c2
Parabola y2 = 4axFocus (a, 0) · directrix x = −a · latus rectum 4a · point (at2, 2at) · focal chord t1t2 = −1, length a(t + 1/t)2 = 4a cosec2θ · focal distance a(1 + t2)
Parabola tangents and normalsTangent ty = x + at2 · y = mx + a/m · normal y = −tx + 2at + at3 · chord subtending 90° at vertex: t1t2 = −4, passes through (4a, 0)
Ellipse x2/a2 + y2/b2 = 1 (a > b)b2 = a2(1 − e2) · foci (±ae, 0) · directrices x = ±a/e · latus rectum 2b2/a · SP + S′P = 2a · point (a cos θ, b sin θ) · tangent y = mx ± √(a2m2 + b2)
Hyperbola x2/a2 − y2/b2 = 1b2 = a2(e2 − 1) · foci (±ae, 0) · latus rectum 2b2/a · |SP − S′P| = 2a · asymptotes y = ±(b/a)x · tangent y = mx ± √(a2m2 − b2) · conjugate hyperbola: 1/e12 + 1/e22 = 1
Rectangular hyperbolaxy = c2 · point (ct, c/t) · e = √2 · tangent x + t2y = 2ct
Area with fociFor P(x1, y1) on an ellipse or hyperbola with foci (±c, 0): area of PSS′ = c|y1|

7. How to Study Coordinate Geometry for JEE — Mastering Each Sub-Topic

This is the core of how to study Coordinate Geometry for JEE: one part at a time, in syllabus order, because each part uses the one before it. Do not move on until you can solve the PYQ types listed under each heading without notes.

Straight Lines (56 Main Qs 2024–26 · 3 Advanced Qs)

Lines are the language of the whole chapter, so build them first and build them properly.

  • Triangle geometry (25 Main Qs): centroid, incentre, circumcentre and orthocentre, area from vertices, and finding a vertex from given medians, altitudes or bisectors. 2025 asked for the distance between the orthocentres of two triangles; 2026 asked for the incentre from the midpoints of the sides.
  • Distances and images (12): distance from a point to a line, between parallel lines, the image of a point and the foot of the perpendicular. Reflection of a light ray from a line was a favourite 2024 numerical.
  • Families and intersections (8): any line through the intersection of L1 and L2 is L1 + λL2 = 0.

Worked example from JEE Main 2025: the family x(3λ + 1) + y(7λ + 2) = 17λ + 5 rearranges to (x + 2y − 5) + λ(3x + 7y − 17) = 0. Every member passes through the intersection of x + 2y = 5 and 3x + 7y = 17, which is (1, 2). The farthest member from a given point is the one perpendicular to the segment joining that point to (1, 2).

Worked example from JEE Main 2024: 20 lines, where the odd-numbered lines are parallel and the even-numbered ones pass through one point. With no restrictions, 20 lines meet in C(20, 2) = 190 points. The 10 parallel lines lose C(10, 2) = 45 points, and the 10 concurrent lines meet in 1 point instead of 45, losing 44 more. The maximum is 190 − 45 − 44 = 101.

Practice target: 40 Straight Lines PYQs, at least half of them triangle questions. Aim for under two minutes each.

Circles (45 Main Qs 2024–26 · 16 Advanced Qs)

Circles bring in the chord results you will reuse for every conic.

  • Finding a circle from conditions (12 Main Qs): through three points, with a given diameter, or touching given lines. For concyclic-point questions (2024 and 2025 both asked one), write the circle through three of the points and substitute the fourth.
  • Intersections and two circles (11): position of a line, length of a chord, common chord, the number of common tangents and the range of r for two circles to meet (2026).
  • Tangents and chords (7): T = 0, T = S1 and the length of the tangent √S1.

Worked example from JEE Main 2025: (4, 6), (−1, 5), (0, 0) and (k, 3) are concyclic. A circle through the origin is x2 + y2 + 2gx + 2fy = 0. Substituting (4, 6) and (−1, 5) gives g = −2 and f = −3, so the circle is x2 + y2 − 4x − 6y = 0. Putting in (k, 3) gives k2 − 4k − 9 = 0.

Practice target: 35 Circles PYQs, including ten on two circles. Learn the common-tangent count table by heart.

"T = 0, T = S1 and SS1 = T2 are the same three results for every curve in this chapter. Learn them once on the circle, and you have already done a quarter of Parabola, Ellipse and Hyperbola." — AKS Yadav Sir, Maths HOD (IIT BHU, AIR 1 FTRE 2009, Ex-Faculty Allen Delhi)

Parabola (43 Main Qs 2024–26 · 18 Advanced Qs)

Parabola is the most-asked conic in JEE Advanced, and it rewards one habit above all: use the parametric point (at2, 2at).

  • Focal properties (14 Main Qs): focus, directrix, latus rectum and focal distance, including shifted parabolas.
  • Chords and intersections (12): focal chords (t1t2 = −1), chords through a fixed point and chords subtending a right angle at the vertex (t1t2 = −4).
  • Tangents and normals (8), areas (5) and locus (4): 2026 alone had 4 locus questions, up from none in 2024 and 2025.

Worked example from JEE Main 2024: a focal chord of y2 = 12x has length 15. Here a = 3, and a focal chord at angle θ to the axis has length 4a cosec2θ = 12 cosec2θ. So sin2θ = 4/5 and tan2θ = 4: the chord has slope ±2, and the rest of the question follows from there.

Worked example from JEE Main 2026: the image of x2 = 4y in the line x − y = 1. Reflection in x − y = 1 sends (x, y) to (y + 1, x − 1). So a point (X, Y) on the image comes from x = Y + 1, y = X − 1 on the parabola, and the image is (Y + 1)2 = 4(X − 1).

Practice target: 35 Parabola PYQs. Solve every chord question with parameters, even when a Cartesian method looks shorter.

Ellipse (41 Main Qs 2024–26 · 13 Advanced Qs)

JEE Main's ellipse questions are mostly about one relation, b2 = a2(1 − e2), used in many disguises.

  • Focal properties (21 Main Qs): eccentricity from a condition, latus rectum, focal distances and SP + S′P = 2a. 2025 and 2024 gave the minor axis as a fraction (¼ or ½) of the distance between the foci; 2025 and 2026 defined the eccentricity through the maximum or minimum of a function.
  • Tangents and chords with a given midpoint (6): T = S1 again, which 2025 asked four times.
  • Locus (5), areas (5) and intersections (4): the parametric point (a cos θ, b sin θ) handles most of these.

When a question gives a relation between the axes and the focal distance, write everything in terms of a and e first. For example, if the minor axis 2b equals half the focal distance 2ae, then b = ae/2, so a2(1 − e2) = a2e2/4 and e2 = 4/5.

Practice target: 30 Ellipse PYQs, including every chord-with-midpoint question from 2024 to 2026.

Hyperbola (33 Main Qs 2024–26 · 10 Advanced Qs)

Hyperbola is the most predictable part in JEE Main: 25 of its 33 questions were focal properties.

  • Confocal conics: 2024 and 2026 gave a hyperbola sharing its foci with a given ellipse. Find c from the ellipse first, then use c2 = a2 + b2 for the hyperbola.
  • Foci not on the axes: 2025 gave foci (1, 14) and (1, −12). The centre is the midpoint (1, 1), 2c = 26, and the transverse axis is vertical. Shift to the centre before using standard results.
  • Areas with the foci (6): the area of triangle PSS′ is c|y1|, which 2024 and 2026 both used.

Worked example from JEE Main 2026: P(10, 2√15) lies on x2/a2 − y2/b2 = 1, whose latus rectum is 8. Then 2b2/a = 8 gives b2 = 4a, and substituting P gives 100/a2 − 15/a = 1, so a2 + 15a − 100 = 0 and a = 5. Then b2 = 20, c = √45 = 3√5, and the area of PSS′ is c · 2√15 = 30√3, so its square is 2700.

Practice target: 25 Hyperbola PYQs. Make a single sheet comparing ellipse and hyperbola results side by side.

That is how to study Coordinate Geometry for JEE part by part. Once you have finished all five, test yourself under exam conditions with our JEE test series, and bring any question that still does not make sense to the JEE Doubt Lab for a 1-on-1 explanation.

Ready for exam-level practice?

Ishaan Singh: AIR 2046 in JEE Advanced 2026 · 99.70 percentile in JEE Main 2026

Parabola is the most-asked conic in JEE Advanced, and common tangents between two curves are where most students lose marks. Practise them 1-on-1 with an IITian Maths HOD.

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8. JEE Advanced Exclusive Topics

If you are deciding how to study Coordinate Geometry for JEE Advanced as well as Main, this section is for you. Advanced uses the same results but goes further in four places.

Common tangents to two curves

Advanced asks for common tangents far more than Main does: two circles (2019, 2023), a circle and a parabola (2018), an ellipse and a parabola (2023), and a circle and a hyperbola (2015). The method is always the same. Write the tangent to one curve in slope form, for example y = mx + a/m for y2 = 4ax, and apply the other curve's tangency condition to it.

Pairs of tangents from an external point

2021 and 2022 each asked about tangents from a point to a parabola, and 2024 asked the same for an ellipse. Use the slope form: the slopes of the two tangents are the roots of a quadratic in m, so their sum and product come straight from the coefficients. 2026 asked about perpendicular tangents to a parabola, which always meet on the directrix; perpendicular tangents to an ellipse meet on the director circle x2 + y2 = a2 + b2.

Circles inside other curves

The largest circle inside a parabolic region (2021), circles touching two sides of a triangle and its circumcircle (2022), and n equal circles touching a larger circle (2022) all need you to write the touching condition as a distance between centres. The 2021 questions on circles Cn and Dn combined this with a geometric progression.

Match-the-columns across all conics

2017, 2018, 2019, 2024 and 2026 used match-the-columns formats, and several of them list properties of different curves together. These test whether you know every standard result, not just the one you used in the last question. The formula table in Section 6 is your checklist.

"In Advanced, almost every question has two curves in it. The skill is not solving one conic; it is moving between them. Write one curve's tangent in slope form and apply the other's condition. That single routine solves a large share of the Advanced papers." — AKS Yadav Sir, Maths HOD (IIT BHU, AIR 1 FTRE 2009, Ex-Faculty Allen Delhi)

9. Revision Checklist

The last step in how to study Coordinate Geometry for JEE is an honest self-check. You should be able to answer "yes" to every line below without notes.

  • ☐ I can find the centroid, incentre, circumcentre and orthocentre of a triangle from its vertices or its sides.
  • ☐ I can find the image of a point in a line and the foot of the perpendicular in one step.
  • ☐ I can find the fixed point of a family of lines L1 + λL2 = 0.
  • ☐ I can write both angle bisectors and tell which one bisects the angle containing a given point.
  • ☐ I know when to use T = 0, T = S1 and SS1 = T2.
  • ☐ I know the number of common tangents of two circles for every position.
  • ☐ I use the parametric point (at2, 2at) for every parabola chord question.
  • ☐ I know t1t2 = −1 for a focal chord and t1t2 = −4 for a chord subtending a right angle at the vertex.
  • ☐ I never confuse b2 = a2(1 − e2) with b2 = a2(e2 − 1).
  • ☐ I check which axis is the major or transverse axis before writing the foci.
  • ☐ I know the tangency condition for a line with a circle, a parabola, an ellipse and a hyperbola.
  • ☐ I can find the area of triangle PSS′ for a point on an ellipse or hyperbola.
  • ☐ I have solved every JEE Main 2024–2026 and JEE Advanced 2015–2026 question from this chapter at least once.

Conclusion

Coordinate Geometry gave JEE Main 218 questions from 2024 to 2026, about one in every seven Maths questions, and JEE Advanced 60 questions from 2015 to 2026, in every single year. In Main, focal properties of conics (60) and triangle geometry (46) gave almost half the questions, and the conics are taking a growing share from lines. In Advanced, tangents and common tangents between two curves dominate. So if you are working out how to study Coordinate Geometry for JEE, the order is clear: build Straight Lines and triangle geometry first, then Circles and the T = S1 family of results, then the three conics with their standard properties, and finish with common tangents and two-curve problems for Advanced.

How we built this data. We went through every JEE Main shift paper from 2024, 2025 and 2026 and every JEE Advanced paper from 2015 to 2026, picked out each question from Straight Lines, Circles, Parabola, Ellipse and Hyperbola, and tagged it by the work it needs. Where the archived text of a question was too incomplete to classify with confidence, we counted it in the totals and said so instead of guessing. Questions that use two curves are counted once, under the chapter the paper archive files them in.

If you want a faculty member to check your preparation, every pack starts with a free 30-minute mentorship call. Straight Lines, Circles, Parabola, Ellipse and Hyperbola each have their own packs on our JEE Maths coaching page, and once your exam is done, our JEE counselling team can help you turn your rank into the right college and branch.

Frequently Asked Questions

How many questions come from Coordinate Geometry in JEE Main?

Counting Straight Lines, Circles, Parabola, Ellipse and Hyperbola across all shifts, JEE Main asked 75 questions in 2024 (about 12.5% of Maths questions), 72 in 2025 (15.2%) and 71 in 2026 (15.0%). That is three to four questions in a typical paper.

Is Coordinate Geometry easy or difficult for JEE?

JEE Main questions are mostly easy to medium: once you know the standard result, the question takes two or three steps. JEE Advanced questions are harder because they combine two curves and ask about common tangents, loci and multi-correct statements. If you follow this guide on how to study Coordinate Geometry for JEE, the Main questions become routine with steady practice.

Is Coordinate Geometry important for JEE 2027?

Yes. It gave 218 JEE Main questions from 2024 to 2026, the largest share of any Maths area, and it was asked in every JEE Advanced exam from 2015 to 2026. The conics, in particular, have been asked more in 2025 and 2026 than in 2024.

Can I skip Coordinate Geometry for JEE?

No. Skipping it gives up three to four questions in a typical JEE Main paper, about one in seven Maths questions. You can, however, prioritise within it: focal properties and triangle geometry are the highest-return topics for Main.

What is the 80/20 rule for how to study Coordinate Geometry for JEE?

Master the focus, eccentricity and latus-rectum results for all three conics, triangle geometry with lines, and intersections and chords. In JEE Main 2024–2026 these three kinds of question gave 142 of the 218 questions, about two-thirds of the chapter. Add locus and distance-and-image questions and you cover 178 of 218.

Which Coordinate Geometry topics are asked mainly in JEE Advanced?

Tangents, normals and common tangents. They appear in well over half of the 60 Advanced questions from 2015 to 2026, compared with about one in ten Main questions. Advanced also combines two curves in one question, asks about circles inside other curves, and uses match-the-columns formats across all the conics. Parabola (18) and Circles (16) were the most-asked parts.

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