Question

Find the coordinates of the point on the parabola $y^2=8x$ whose focal distance is $8$.

Answer 1

Given Parabola: $y^2=8x..........\left(1\right)(a=2)$

Let there be a point $(x_1,y_1)$ with focal distance $8$.

Now focal distance of $(x_1,y_1)=x_1+a=8$

$=>x_1+2=8$

$=>x_1=6$

Now, $y_1^2=8x_1$

$=>y_1^2=8\left(6\right)$

$=>y_1=\pm \sqrt{48}$

$=>y_1=\pm 4\sqrt{3}$

now points are $(6,4\sqrt{3})$ and $(6,-4\sqrt{3})$ having focal distance $=8$