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AP EAMCET2006MathematicsApplication of Derivatives

If is the angle between the curves x y=2 and x^2+4 y=0 and x^2+4 y=0 , then is equal to :

Options

  1. A1
  2. B-1
  3. C2
  4. D3

Correct answer

D. 3

Step-by-step solution

The equation of curves are x y=2 (i) and x^2+4 y=0 (ii) On solving Eqs. (i) and (ii), we get Point of intersection which is (2,-1) . From Eq. (i) x d y d x +y=0 d y d x =- y x m₁= ( d y d x )_ (2,-1) = 1 2 and From Eq. (ii), 2 x+4 d y d x =0 m₂=-1 = | m₁-m₂ 1+m₁ m₂ |= | 1 2 +1 1- 1 2 |= | 3 2 1 2 | =3

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