PYQ Vault
EbooksTutor

Equation of the tangent or normal to a parametric curve at a given parameter

This type of question, asked 6 times: 2 May 2023 S2, 3 May 2023 S1, 9 May 2023 S2, 11 May 2023 S1, 16 Apr 2026 S2, 18 Apr 2026 S1. All 6 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2 May 2023 S2

    139
    The equation of normal to the curve x=θ+sin⁡θ,  y=1+cos⁡θx=\theta+\sin\theta,\; y=1+\cos\theta at θ=π2\theta=\frac{\pi}{2} is

    Tap an option to check your answer.

  2. Question 2

    3 May 2023 S1

    135
    The equation of the normal to the curve x=θ+sin⁡θ, y=1+cos⁡θx=\theta+\sin\theta,\ y=1+\cos\theta at θ=π2\theta=\frac{\pi}{2} is

    Tap an option to check your answer.

  3. Question 3

    9 May 2023 S2

    130
    The equation of the tangent to the curve x=acos⁡3θ,y=asin⁡3θx = a\cos^3\theta, y = a\sin^3\theta at θ=π4\theta = \frac{\pi}{4} is

    Tap an option to check your answer.

  4. Question 4

    11 May 2023 S1

    118
    If equation of normal to the curve x=tx = \sqrt{t}, y=t−1ty = t - \frac{1}{\sqrt{t}} at t=4t = 4 is

    Tap an option to check your answer.

  5. Question 5

    16 Apr 2026 S2

    76
    The equation of tangent to the curves x=1−3t2x = 1 - 3t^2 and y=t−3t3y = t - 3t^3 at the point (−2,2)(-2, 2) is...

    Tap an option to check your answer.

  6. Question 6

    18 Apr 2026 S1

    76
    If the line x+By+C=0x + By + C = 0 is the normal to the curve given by x=asin⁡3t,y=bcos⁡3tx = a\sin^3 t, y = b\cos^3 t, (where a,b≠0a, b \neq 0) at a point t=π2t = \dfrac{\pi}{2}, then B−C=B - C =

    Tap an option to check your answer.