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AP EAMCET2008MathematicsApplication of Derivatives

The equation of the normal to the curve y^4=a x^3 at (a, a) is

Options

  1. Ax+2 y=3 a
  2. B3 x-4 y+a=0
  3. C4 x+3 y=7 a
  4. D4 x-3 y=0

Correct answer

C. 4 x+3 y=7 a

Step-by-step solution

Given curve is y^4=a x^3 On differentiating w.r.t. x , we get aligned & 4 y^3 d y d x =3 a x^2 & ( d y d x )_ (a, a) = 3 a^3 4 a^3 = 3 4 & aligned Equation of normal at point (a, a) is array cc & y-a=- 4 3 (x-a) & 4 x+3 y=7 a array

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