Question

Find equation of parabola with the focus $(2,0)$ and directrix $x=-2$.

Answer 1

Since focus lies on $x$-axis.

Hence equation is either $y^2=4ax$ or $y^2=-4ax$.

Now the focus has a positive x coordinate.

So, we have to use equation $y^2=4ax$.

Coordinates of focus $=(a,0)$

$(2,0)=(a,0)$

Hence

$a=2$

Required equation is

$y^2=4ax$

$y^2=\mathrm{4.2.}x$

$y^2=8x$.