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AP EAMCET2008MathematicsApplication of Derivatives

The angle between the curves y^2=4 x+4 and y^2=36(9-x) is

Options

  1. A30^
  2. B45^
  3. C60^
  4. D90^

Correct answer

D. 90^

Step-by-step solution

Given curves are y^2=4 x+4 and y^2=36(9-x) On solving, we get the points (8,6) and (8,-6) . On differentiating Eq. (i), we get aligned & 2 y d y d x =4 and 2 y d y d x =-36 & d y d x = 2 y and d y d x = -18 y aligned At point (8,6) , aligned & m₁= d y d x = 2 6 = 1 3 and m₂= d y d x = -18 6 =-3 & = 1 3 +3 1+ 1 3 (-3) = 10 / 3 0 = & = 2 aligned And at point (8,-6) , aligned & m₁= d y d x = 2 -6 =- 1 3 and m₂= d y d x = -18 -6 =3 & = |- 1 3 -3 | 1+ (- 1 3 ) 3 = 10 / 3 0 = & = 2 aligned

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