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Conic Sections

JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 8 times: 27 Jan 2024, 29 Jan 2024, 4 Apr 2024, 23 Jan 2025, 24 Jan 2025, 28 Jan 2025, 29 Jan 2025, 21 Jan 2026 S1. This one: 21 Jan 2026 S1 See all 8 of this type

    70
    Let O be the vertex of the parabola x2=4yx^{2}= 4y and Q be any point on it. Let the locus of the point P , which divides the line segment OQ internally in the ratio 2: 3 be the conic C . Then the equation of the chord of C , which is bisected at the point (1,2)(1,2), is:

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  2. Question 2

    This type asked 7 times: 2021 Paper 7, 2021 Paper 9, 15 Apr 2023, 30 Jan 2024, 1 Feb 2024, 22 Jan 2025, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 7 of this type

    62
    Let the set of all values of r , for which the circles (x+1)2+(y+4)2=r2(x + 1)^{2}+ (y + 4)^{2}=r^{2} and x2+y2−4x−2y−4=0x^{2}+y^{2}- 4x - 2y - 4 = 0 intersect at two distinct points be the interval ( α\alpha, β\beta ). Then αβ\alpha\beta is equal to

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  3. Question 3

    This type asked 6 times: 2021 Paper 4, 25 Jun 2022, 26 Jun 2022, 28 Jul 2022, 30 Jan 2023, 10 Apr 2023. This one: 10 Apr 2023 See all 6 of this type

    84
    Let a common tangent to the curves y2=4xy^{2}= 4x and (x−4)2+y2=16(x - 4)^{2}+y^{2}= 16 touch the curves at the points PP and QQ. Then (PQ)2(PQ)^{2} is equal to

  4. Question 4

    This type asked 5 times: 25 Jul 2022, 31 Jan 2024, 9 Apr 2024, 21 Jan 2026 S1, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 5 of this type

    60
    Let the ellipse E:x2144+y2169=1E:\frac{x^{2}}{144}+\frac{y^{2}}{169}= 1 and the hyperbola H:x216−y2λ2=−1H:\frac{x^{2}}{16}-\frac{y^{2}}{\lambda^{2}}= - 1 have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H , then the value of 24(e+L)24(e + L) is :

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  5. Question 5

    This type asked 5 times: 14 Jun 2022, 28 Jun 2022, 25 Jul 2022, 13 Apr 2023, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 5 of this type

    60
    If the line αx+2y=1\alpha x + 2y = 1, where α∈R\alpha \in R, does not meet the hyperbola x2−9y2=9x^{2}- 9y^{2}= 9, then a possible value of α\alpha is :

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  6. Question 6

    This type asked 5 times: 27 Jun 2022, 28 Jun 2022, 27 Jul 2022, 24 Jan 2025, 7 Apr 2025. This one: 7 Apr 2025 See all 5 of this type

    55
    Let PP be the parabola, whose focus is (−2,1)\left( - 2,1 \right) and directrix is 2x+y+2x+y+ 2=02 = 0. Then the sum of the ordinates of the points on P , whose abscissa is -2 , is.

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  7. Question 7

    This type asked 5 times: 2021 Paper 1, 2021 Paper 23, 2021 Paper 26, 26 Jun 2022, 10 Apr 2023. This one: 10 Apr 2023 See all 5 of this type

    157
    Let AA be the point (1,2)(1,2) and BB be any point on the curve x2+y2=16x^{2}+y^{2}= 16. If the centre of the locus of the point PP, which divides the line segment ABAB in the ratio 3:23:2 is the point C(α,β)C(\alpha,\beta), then the length of the line segment ACAC is

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  8. Question 8

    This type asked 5 times: 2021 Paper 8, 2021 Paper 23, 29 Jun 2022, 28 Jul 2022, 6 Apr 2023. This one: 6 Apr 2023 See all 5 of this type

    167
    If the tangents at the points PP and QQ on the circle x2+y2−2x+y=5x^{2}+y^{2}- 2x + y = 5 meet at the point R(94,2)R\left( \frac{9}{4},2 \right), then the area of the triangle PQRPQR is

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  9. Question 9

    This type asked 4 times: 29 Jan 2025, 2 Apr 2026 S1, 2 Apr 2026 S2, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 4 of this type

    72
    Let the centre of the circle x2+y2+2gx+2fy+25=0x^{2} + y^{2} + 2gx + 2fy + 25 = 0 be in the first quadrant and lie on the line 2x−y=42x - y = 4. Let the area of an equilateral triangle inscribed in the circle be 27327\sqrt{3}. Then the square of the length of the chord of the circle on the line x=1x = 1 is____\_\_\_\_ .

  10. Question 10

    This type asked 4 times: 31 Jan 2023, 22 Jan 2025, 2 Apr 2025, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 4 of this type

    63
    Let the eccentricity e of a hyperbola satisfy the equation 6e2−11e+3=06e^{2}- 11e + 3 = 0. If the foci of the hyperbola are (3,5)(3,−4)(3,5)(3, - 4), then the length of its latus rectum is:

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