PYQ Vault

Angle between two curves at their point of intersection

This type of question, asked 4 times: 16 May 2023 S1, 12 May 2024 S1, 19 Apr 2025 S1, 25 Apr 2025 S2. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    16 May 2023 S1

    117
    If θ\theta denotes the acute angle between the curves y=10−x2y = 10 - x^2 and y=2+x2y = 2 + x^2, at a point of the intersection, then ∣tan⁡θ∣|\tan\theta| is equal to

    Tap an option to check your answer.

  2. Question 2

    12 May 2024 S1

    111
    The angle between the tangents to the curves y=2x2y=2x^{2} and x=2y2x=2y^{2} at (1,1)(1,1) is

    Tap an option to check your answer.

  3. Question 3

    19 Apr 2025 S1

    140
    The angle between the curves xy=6xy= 6 and x2y=12x^{2}y= 12 is

    Tap an option to check your answer.

  4. Question 4

    25 Apr 2025 S2

    141
    The angle θ\theta, at which the curves y=3xy=3^{x} and y=7xy=7^{x} intersect, is given by

    Tap an option to check your answer.