An angle of intersection of the curves, x 2 a 2 + y 2 b 2 = 1 and x 2 + y 2 = a b , a > b , is :

Step-by-step solution

Given equations are x 2 a 2 + y 2   b 2 = 1   . . . 1 and x 2 + y 2 = a b . . . . . 2   where   a > b . From 1 , b 2 x 2 + a 2 y 2 = a 2 b 2 Substituting value of y 2 from 2 in the above equation b 2 x 2 + a 2 a b - x 2 = a 2 b 2 ⇒ b 2 - a 2 x 2 = a 2 b 2 - a 3 b ⇒ x 2 = b a 2 b - a b 2 - a 2 = a 2 b a + b ∴ x = a 2 b a + b Substituting value of x 2 in 2 , we get y 2 = a b 2 a + b ∴ y = a b 2 a + b Point of intersection is a 2 b a + b ,   a b 2 a + b Now, from 1