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AP EAMCET2013MathematicsApplication of Derivatives

If the curves x^2+p y^2=1 and q x^2+y^2=1 are orthogonal to each other, then

Options

  1. Ap-q=2
  2. B1 p - 1 q =2
  3. C1 p + 1 q =-2
  4. D1 p + 1 q =2

Correct answer

D. 1 p + 1 q =2

Step-by-step solution

Given curves are aligned & x^2+p y^2=1 & q x^2+y^2=1 aligned and On differentiating Eq. (i), w.r.t., x we get gathered 2 x+2 y p d y d x =0 d y d x =m₁=- x p y gathered On differentiating Eq. (ii), w.r.t. to x , we get array r 2 q x+2 y d y d x -0 d y d x =m₂= -q x y array Since, both the curves are orthogonal to each other, Then, -x p y -q x y =-1 q x^2=-p y^2 q (1-p y^2 )=-p y^2 [from Eq. (i)] q-p q y^2=-p y^2 q=(p q-p)=y^2 y^2= q p q-p and x^2= -p p q-p On putting x^2 and y^2 in Eq. (ii) we get array cc & - p q

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