If the normals at two points P and Q of a parabola y 2 = 4 x intersect at a third point R on the parabola y 2 = 4 x , then the product of the ordinates of P and Q is equal to

Step-by-step solution

Let, P = t 1 2 , 2 t 1 , Q = t 2 2 , 2 t 2 and R = t 2 , 2 t then t 1 , t 2 are roots of the equation t = - x - 2 x ⇒ t 1 , t 2 are roots of the equation x 2 + t x + 2 = 0 ⇒ t 1 t 2 = 2 ⇒ 2 t 1 2 t 2 = 8 ⇒ product of the ordinates of P and Q is equal to 8