Question

Find the coordinates of points on the parabola $y^2=8x$ whose focal distance is 4.

Answer 1

Given parabola $y^2=8x$

On comparing this parabola to the $y^2=4ax$ we get

8x=4ax $\Rightarrow a=2$

$\therefore Focaldistance=|x+a|=4\Rightarrow |x+2|=4\Rightarrow x+2=\pm 4\Rightarrow x=2,-6Butx\ne -6Forx=2,y^2=8\times 2\therefore y^2=16\Rightarrow \times y=\pm 4$

So,the points are (2,4) and (2,-4).