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AP EAMCET202119 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

If the curves x 2 a 2 + y 2 4 = 1 and y 3 = 16 x intersect at right angles, then a 2 =

Options

  1. A2 3
  2. B2 3
  3. C4 3
  4. D3 4

Correct answer

C. 4 3

Step-by-step solution

We have curves x 2 a 2 + y 2 4 = 1 and y 3 = 16 x , Let, these two curves intersect at x 1 ,   y 1 Slope of tangent at point x 1 ,   y 1 in the curve x 2 a 2 + y 2 4 = 1 y 2 4 = 1 - x 2 a 2   ⇒   2 y 4 × d y d x = - 2 x a 2   ⇒   d y d x x 1 ,   y 1 = m 1 x 1 ,   y 1 = - 4 x 1 y 1 a 2 Slope of tangent at a point in the curve: y 3 = 16 x 3 y 2 d y d x = 16   ⇒   d y d x x 1 ,   y 1 = m 2 x 1 ,   y 1 = 16 3 y 1 2 These curves intersect

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