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NDA2015MathematicsDifferentiationActual

Consider the parametric equation x= a (1-t^2 ) 1+t^2 , y= 2 a t 1+t^2 What is d^2 y d x^2 equal to?

Options

  1. Aa^2 y^2
  2. Ba^2 x^2
  3. C- a^2 x^2
  4. D- a^2 y^3

Correct answer

D. - a^2 y^3

Step-by-step solution

d^2 y d x^2 = y d d x (-x)-(-x) d y d x y^2 aligned & = -y+x d y d x y^2 = -y+x ( -x y ) y^2 & = -y^2-x^2 y^3 = - (x^2+y^2 ) y^3 =- a^2 y^3 aligned Option (D) is correct.

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