PYQ Vault

Conic Sections

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET 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

    Asked 4 times: 20 Apr 2025 S1*, 13 Apr 2026 S1*, 12 May 2026 S1*, 19 May 2026 S1 (* = numbers or wording changed that year) See all 4 times it was asked

    63
    The area (in sq.units) of a triangle formed by joining the vertex and the endpoints of the latus rectum of the parabola x2=−20yx^2 = -20y is...

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  2. Question 2

    This type asked 4 times: 22 Apr 2025 S1, 26 Apr 2025 S2, 17 Apr 2026 S1, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 4 of this type

    59
    A tangent having slope −12-\dfrac{1}{2} to the ellipse 3x2+4y2=123x^2 + 4y^2 = 12 intersects the X-axis and Y-axis at the points A and B respectively. if O is the origin, then the area of △AOB\triangle AOB is ...

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  3. Question 3

    This type asked 3 times: 15 May 2023 S1, 22 Apr 2025 S1, 15 May 2026 S1. This one: 15 May 2026 S1 See all 3 of this type

    59
    The tangent to the parabola x2=2yx^2 = 2y at point P makes an angle of 45∘45^\circ with the X-axis, then the coordinates of P are:

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  4. Question 4

    This type asked 3 times: 16 Apr 2026 S1, 17 Apr 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 3 of this type

    60
    If the line 12x−5y+k=012x - 5y + k = 0 is tangent to the hyperbola x2−4y2=100x^2 - 4y^2 = 100, then k=k =

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  5. Question 5

    Asked 2 times: 19 Apr 2025 S1, 13 May 2026 S1 See all 2 times it was asked

    61
    In an ellipse with semi-minor axis OB, S and S' are its foci, a>ba > b and ∠SBS′\angle SBS' is a right angle, then the eccentricity of the ellipse is..

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  6. Question 6

    This type asked 2 times: 21 Apr 2025 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 2 of this type

    56
    The equation of the common tangent to the parabolas y2=4xy^2 = 4x and x2=32yx^2 = 32y is ...

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  7. Question 7

    This type asked 2 times: 26 Apr 2025 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 2 of this type

    62
    The equation of the directrix of the parabola x2−4x−5y−1=0x^2 - 4x - 5y - 1 = 0 is...

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  8. Question 8

    This type asked 2 times: 19 Apr 2025 S2, 19 Apr 2026 S2. This one: 19 Apr 2026 S2 See all 2 of this type

    58
    The eccentricity of the ellipse represented by the equation 7x2+16y2−14x+64y−377=07x^2 + 16y^2 - 14x + 64y - 377 = 0 is...

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  9. Question 9

    This type asked 2 times: 12 May 2024 S2, 19 Apr 2025 S2. This one: 19 Apr 2025 S2 See all 2 of this type

    150
    If two curves x2−4y2=2x^{2}- 4y^{2}= 2 and 8x2=40−my28x^{2}= 40 - my^{2} are orthogonal to each other then m=m =

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  10. Question 10

    Asked once: 17 Apr 2026 S1 (same type asked 4 times) See all 4 of this type

    59
    The equations of the tangents to the ellipse x216+y29=1\dfrac{x^2}{16} + \dfrac{y^2}{9} = 1 making an inclination of 30∘30^\circ with the major axis are

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