Let R be the focus of the parabola y 2 = 20 x and the line y = m x + c intersect the parabola at two points P and Q . Let the points G 10 , 10 be the centroid of the triangle P Q R . If c - m = 6 , then P Q 2 is

Step-by-step solution

Given, R be the focus of the parabola y 2 = 20 x and the line y = m x + c intersect the parabola at two points P and Q , And the points G 10 ,   10 be the centroid of the triangle P Q R , Now focus of the parabola y 2 = 20 x will be, R 5 , 0 And parametric points of P Q be 5 t 2 , 10 t , Now plotting the diagram we get, Now finding the centroid of the triangle we get, For x - coordinate we get, ⇒ 5 t 1 2 + 5 t 2 2 + 5 3 = 10 ⇒ t 1 2 + t 2 2 = 5               . . .