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COMEDK2012MathematicsApplication of Derivatives

If the tangent to the curve 2 y³=a x²+x³ at the point (a, a) cuts off intercepts and on the coordinate axes, where ²+ ²=61 , then the value of a is equal to

Options

  1. A25
  2. B36
  3. C30
  4. D40

Correct answer

C. 30

Step-by-step solution

Given, equation of curve is 2 y³=a x²+x³ 6 y² d y d x =2 a x+3 x² d y d x = 2 a x+3 x² 6 y² . d y d x |_ (a, a) = 2 a²+3 a² 6 a² = 5 a² 6 a² = 5 6 So, x -intercept =- a 5 = and y -intercept = a 6 = ²+ ²=61 a² 25 + a² 36 =61 61 a² 36 25 =61 a²=36 25 a= 6 5= 30

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