Question

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

Answer 1

Let the point on the parabola $y^2=8x$ be $P(x,y).$
Then its focal distance is $SP=x+a$.
Here, $a=2\text{and}SP=4.$
$\therefore 4=x+2$
$\Rightarrow x=2$
$\Rightarrow y^2=8\times 2$
$\Rightarrow y=\pm 4$
Thus, the coordinates of the required points are $(2\pm 4)$.