Question

Coordinates of a point on the parabola $y^2=8x$ whose focal distance is $4$, are

Answer 1

If the coordinates of a point on the parabola $y^2=8x$ are $P(x,y)$, then its focal distance $SP=x+a$ where $S$ is the focus of the parabola.

Here, $a=2$ and $SP=4$
$\Rightarrow 4=x+2$
$\Rightarrow x=2$
$\Rightarrow y^2=8\left(2\right)$
$\Rightarrow y=\pm 2$

Thus, the coordinates of the required point are $(2,\pm 4)$