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AP EAMCET2002MathematicsApplication of Derivatives

The two curves x=y^2, x y=a^3 cut orthogonally at a point, then a^2 is equal to

Options

  1. A1 3
  2. B1 2
  3. C1
  4. D2

Correct answer

B. 1 2

Step-by-step solution

We have, x=y^2 2 y d y d x =1 d y d x = 1 2 y and x y=a^3 x d y d x +y=0 d y d x =- y x On solving equations (i) and (ii), we get the point of intersection (a^2, a ) aligned m₁ & = ( d y d x )_ (a^2, a ) = 1 2 a^ and m₂ & = ( d y d x )_ (a^2, a ) = -a a^2 =- 1 a aligned Since, curves cut orthogonally then, array lrl m₁ m₂=-1 & & ( 1 2 a ) (- 1 a ) & =-1 & a^2 & = 1 2 array

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