JEE Main Maths · Conic Sections

General Conic Section in JEE Main

Name: General Conic Section: JEE Main previous year questions
Creator: Lumi

General Conic Section (Maths, Conic Sections) came 14 times in 12 of the 42 JEE Main shifts Lumi analysed, across 6 distinct ideas. 8 of them came in 2024–26; it was last asked in 2026.

Questions: 14; in 12 shifts
Ideas asked: 6; 3 asked more than once
Numerical answer: 5; 36% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 0Medium 7Hard 7

Format

Single correct9 Q
Numerical value5 Q

Ideas inside the topic

6 ideas

Condition for Line to be Tangent5 Q
Chord Bisected at a Given Point (T=S1)4 Q
Chord of Contact for General Conic2 Q
Family of Conics: Intersection of Two Conics1 Q
Focus-Directrix Form Extraction1 Q
Vertex of Parabola from General Equation1 Q

Where it sits

Part of Conic Sections, which had 116 questions in all. General Conic Section accounts for 12% of them. In Lumi's JEE taxonomy it belongs to Coordinate Geometry.

Every question

All 14 General Conic Section questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 2 · Q11Let $O$ be the origin, and $P$ and $Q$ be two points on the rectangular hyperbola $xy = 12$ such that the midpoint of the line segment…MediumSingle correct
4 Apr 2026, Shift 1 · Q13Suppose that two chords, drawn from the point $(1,2)$ on the circle $x^2+y^2+x-3y=0$ are bisected by the $y$ -axis. If the other ends of…HardSingle correct
5 Apr 2026, Shift 1 · Q10Let P be a moving point on the circle $x^2 + y^2 - 6x - 8y + 21 = 0$ . Then, the maximum distance of P from the vertex of the parabola…MediumSingle correct
6 Apr 2026, Shift 2 · Q12Let $x=9$ be a directrix of an ellipse E, whose centre is at the origin and eccentricity is $\frac{1}{3}$ . Let P $(\alpha,0)$ , $\alpha>0$ ,…MediumSingle correct
4 Apr 2025, Shift 2 · Q10Let for two distinct values of p the lines $y=x+p$ touch the ellipse $E:\frac{x^2}{4^2}+\frac{y^2}{3^2}=1$ at the points A and B. Let the…HardSingle correct
7 Apr 2025, Shift 1 · Q10Let P be the parabola, whose focus is $(-2, 1)$ and directrix is $2x + y + 2 = 0$ . Then the sum of the ordinates of the points on P, whose…MediumSingle correct
9 Apr 2024, Shift 2 · Q27Consider the circle $C: x^2+y^2=4$ and the parabola $P: y^2=8x$ . If the set of all values of $\alpha$ , for which three chords of the…HardNumerical value
29 Jan 2024, Shift 1 · Q28If the points of intersection of two distinct conics $x^2+y^2=4b$ and $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ lie on the curve $y^2=3x^2$ , then…HardNumerical value
25 Jul 2022, Shift 1 · Q28Let the equation of two diameters of a circle $x^2+y^2-2x+2fy+1=0$ be $2px-y=1$ and $2x+py=4p$ . Then the slope $m\in(0,\infty)$ of the…MediumNumerical value
28 Jul 2022, Shift 1 · Q11If the tangents drawn at the points P and Q on the parabola $y^2=2x-3$ intersect at the point R(0, 1), then the orthocentre of the…HardSingle correct
28 Jul 2022, Shift 1 · Q27For the hyperbola $H:x^2-y^2=1$ and the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b>0$ , let the (1) eccentricity of E be reciprocal…HardNumerical value
24 Jun 2022, Shift 1 · Q15Let $\lambda x-2y=\mu$ be a tangent to the hyperbola $a^2x^2-y^2=b^2$ . Then…MediumSingle correct
24 Jun 2022, Shift 1 · Q28If two tangents drawn from a point $(\alpha, \beta)$ lying on the ellipse $25x^2+4y^2=1$ to the parabola $y^2=4x$ are such that the slope…HardNumerical value
3 Aug 2021, Shift 2 · Q75The tangents, to the parabola $y^2 = 2 - x$ at the points of its intersection with the line $y = x - 2$ , intersect at the pointMediumSingle correct