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COMEDK2013MathematicsApplication of Derivatives

If tangent to the curve x=a t², y=2 a t is perpendicular to X -axis, then its point of contact is

Options

  1. A(a, a)
  2. B(0, a)
  3. C(0,0)
  4. D(a, 0)

Correct answer

C. (0,0)

Step-by-step solution

We have, x=a t², y=2 a t Now, d x d t =2 a t, d y d t =2 a d y d x = d y / d t d x / d t = 2 a 2 a t = 1 t Since, tangent is perpendicular to X -axis, then d y d x = 1 0 1 t = 1 0 t=0 x=a t²=0 and y=2 a t=0 So, required point is (0,0) .

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