Question

Find the co-ordinates of the points on the parabola $y^2=8x$, whose focal distance is $10$

Answer 1

Comparing above parabola with $y^2=4ax$, we get $a=2$

So focal distance is given by, $x+a=10$ (given )

$\Rightarrow x+2=10\Rightarrow x=8$

Substitute $x=8$ in the given parabola,

$y^2=8x=8^2\Rightarrow y=\pm 8$

Hence coordinate of the points on the parabola whose focal distance is $10$ units are $(8,8)$ and $(8,-8)$