PYQ Vault
EbooksTutor

Angle between two conics at a point where they meet

This type of question, asked 4 times: 2021 Paper 3, 2021 Paper 23, 2021 Paper 24, 6 Apr 2023. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 3

    75
    If the curves, x2a+y2b=1\frac{x^{2}}{a}+\frac{y^{2}}{b}= 1 and x2c+y2d=1\frac{x^{2}}{c}+\frac{y^{2}}{d}= 1 intersect each other at an angle of 90∘90^{\circ}, then which of the following relations is true?

    Tap an option to check your answer.

  2. Question 2

    2021 Paper 23

    71
    The angle of intersection of the curves x2a2+y2b2=1\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 and x2+y2=ab, a>b,x^{2}+y^{2}=ab,\ a>b, is:

    Tap an option to check your answer.

  3. Question 3

    2021 Paper 24

    80
    Let θ\theta be the acute angle between the tangents to the ellipse x29+y21=1\frac{x^{2}}{9}+\frac{y^{2}}{1}= 1 and the circle x2+y2=3x^{2}+y^{2}= 3 at their point of intersection in the first quadrant. Then tan⁡θ\tan\theta is equal to:

    Tap an option to check your answer.

  4. Question 4

    6 Apr 2023

    179
    Let the eccentricity of an ellipse x2a2+y2b2=1\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1 is reciprocal to that of the hyperbola 2x2−2y2=12x^{2}- 2y^{2}= 1. If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is