If the curves y 2 = 6 x , 9 x 2 + b y 2 = 16 intersect each other at right angles, then the value of b is:

Step-by-step solution

Given, curves y 2 = 6 x and 9 x 2 + b y 2 = 16 Let the point of intersection of curves be x 1 ,   y 1 . So, 2 y 1 d y d x = 6 ⇒     d y d x = 3 y 1 18 x 1 + 2 b y 1 d y d x = 0 ⇒     d y d x = - 9 x 1 b y 1 Since both the curve intersect at right angle. 3 y 1 × - 9 x 1 b y 1 = - 1 ⇒ 27 x 1 = b y 1 2 (Since y 1 2 = 6 x 1 ) ⇒ 27 x 1 = b 6 x 1 x 1 ≠ 0 b = 27 6 = 9 2