JEE Advanced Conic Sections questions with solutions
Parabola, ellipse and hyperbola. 39 questions from our 2016–2025 JEE Advanced pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.
Also practise: Conic Sections for JEE Main · Conic Sections for NDA
JEE Advanced 2025
- Let PQ be the focal chord of the parabola y^2=8x with P=(8,8), where F is the focus.
- Match each conic in List-I with its eccentricity in List-II. List-I (P) An ellipse whose latus rectum is half of its minor axis (Q) A hyperbola whose…
- The normal to the parabola y^2=4x at the point (4,4) meets the parabola again at a point Q. Let Δ1 be the area of the region bounded by this normal…
- A tangent at a point P in the first quadrant of the ellipse (x^2/(25)+(y^2/(16)=1 meets the coordinate axes at A and B. When the length AB is…
JEE Advanced 2024
- The parabola y^2=8x has a focal chord PQ with P=(18,12).
- List-I P. Eccentricity of the conic 9x^2+16y^2-18x+64y-71=0 Q. Eccentricity of the hyperbola conjugate to (x^2/(9)-(y^2/(16)=1 R. Distance between…
- The tangent at a point P in the first quadrant on the ellipse (x^2/(9)+(y^2/(4)=1 meets the coordinate axes at A and B. When the area of triangle OAB…
JEE Advanced 2023
JEE Advanced 2022
- Let P and Q be the end points of the focal chord of the parabola y^2=8x with P=(8,8). Let the tangents at P and Q meet at M.
- Match the geometric quantities in List-I with the values in List-II. List-I (P) Length of the chord of the ellipse (x^2/(25)+(y^2/(9)=1 through the…
- The parabola y^2=4x and the ellipse (x^2/(4)+(y^2/(3)=1 have exactly two common tangents. These two tangents together with the y-axis form a…
- Let E be the ellipse (x^2/(16)+(y^2/(7)=1 with foci F1,F2.
JEE Advanced 2021
JEE Advanced 2020
JEE Advanced 2019
JEE Advanced 2018
- (x^2/(16)+(y^2/(9)=1 with foci S and S'.
- Consider the hyperbola H: (x^2/(9)-(y^2/(16)=1.
- Paragraph 2: Consider the parabola y^2=4x and a focal chord PQ with P=(t^2,2t), t>0, and Q the other end of the chord. The tangents to the parabola…
- Let P be the point (8,8) on the parabola y^2=8x, and let the focal chord through P meet the parabola again at Q.
- Tangent lines are drawn to the ellipse (x^2/(25)+(y^2/(16)=1 at points of the first quadrant. Each tangent cuts off a segment between the coordinate…
- (x^2/(25)+(y^2/(16)=1. List-I (P) The product of the perpendicular distances from the two foci of E to a variable tangent of E. (Q) The radius of the…
JEE Advanced 2017
- From the point T(-6,1), two tangents are drawn to the parabola y^2=4x, touching it at A and B.
- The foci of a hyperbola are S and S' with SS'=10. A point P on the hyperbola satisfies PS⊥ PS' and PS· PS'=18. If the transverse axis of the…
- Paragraph 1: Column 1 lists four curves, Column 2 lists four straight lines and Column 3 lists four points. Each curve in Column 1 is touched by…
- Paragraph 1: The parabola mathcal P: y^2=8x has its focus at F(2,0). A point on it is written parametrically as (2t^2,4t). For a chord PQ of mathcal…
JEE Advanced 2016
- The normal to the parabola y^2=4x at the point P(4,4) meets the parabola again at Q. The area of the region bounded by the parabola and the chord PQ…
- (x^2/(16)+(y^2/(9)=1 with foci F1,F2.
- Let E: (x^2/(16)+(y^2/(9)=1.
- Paragraph 1: Consider the parabola y^2=4x with focus F. A focal chord PQ of the parabola, with P in the first quadrant, satisfies FP=4 FQ. The…
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