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

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