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MHT CET202013 Oct 2020Morning ShiftMathematicsApplication of DerivativesActual

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

Options

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

Correct answer

B. (0,0)

Step-by-step solution

Given equation of curve represents parabola y²=4 a x Given is that tangent is er to X -axis. Therefore point of contact is vertex of parabola which is origin. This problem can also be solved as We have x=a t² and y=2 at dx dt =2 at and dy dt =2 a dy dx = 2 a 2 at = 1 t Slope of tangent = 1 t . Since tangent is Perpendicular to X axis, it is parallel to Y axis i.e. it's slope is indefinite. It means t =0 x =0 and y =0

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