If the curves, x 2 a + y 2 b = 1 and x 2 c + y 2 d = 1 intersect each other at an angle of 90 ° , then which of the following relations is TRUE?

Step-by-step solution

Given curves, x 2 a + y 2 b = 1   . . . . . i On differentiating equation i , we get 2 x a + 2 y b d y d x = 0 ⇒ m 1 = d y d x = - x b y a   . . . i i i and x 2 c + y 2 d = 1 . . . . . i i On differentiating equation i i , we get 2 x c + 2 y d d y d x = 0 ⇒ m 2 = d y d x = - x d y c   . . . i v For orthogonal curves, m 1 × m 2 = - 1 ⇒ - x b y a × - x d y c = - 1 x 2 y 2 = - a c b d . . . . v From equation i - i i , we get x 2 c - a a c = y 2 b - d b d ⇒ x 2 y 2 = b -