Question

If $(x_1,y_1)$ and $(x_2,y_2)$ are the end points of the focal chord of parabola $y^2=16x$, then the value of $16x_1{x}_2+y_1{y}_2$ is

Answer 1

Given parabola is $y^2=16x$
$a=4t_1{t}_2=-1$
Then the coordinates of the end point of the focal chord is
$(x_1,y_1)=(4t_1^2,8t_1)(x_2,y_2)=(\frac{4}{t_1^2},-\frac{8}{t_1})$

Therefore,
$16x_1{x}_2+y_1{y}_2=16\left(16\right)-64=192$