Question

Let the point P of the focal chord PQ of the parabola \(y^2 = 16x\) be (1, -4). If the focus of the parabola divides the chord PQ in the ratio m : n, gcd (m, n) = 1 , then \(m ^ 2 + n ^ 2\) is equal to

(1) 17

(2) 10

(3) 37

(4) 26

Answer 1

Correct option is: (1) 17 

\(P(at^2, 2at) \Rightarrow P(4t^2, 8t) = (1, -4)\)  

\(\Rightarrow t = \frac{-1}{2};\ Q(\frac{a}{t^2}, \frac{-2a}{t})\) 

S(4, 0) is the focus