Ask Me Help Desk - Determine the focus & directrix of the given parabola when why square =2x

There are several examples already posted. Search through existing posts.

But, since I am here.

$y^{2}=2x$

A parabola has this form when it

opens in the positive x direction.

$y^{2}=4px$

Since, in this case, $4p=2$ , then $p=\frac{1}{2}$

p is the distance from the vertex to the focus and from the vertex to the directrix.

Thus, the distance from the focus to the directrix is 2p.

The vertex is at the origin.

This means the focus is at (1/2,0) and the directrix is at (-1/2,0)

That's all there is to it.

If the equation were in the form $y^{2}=-4px$ , then it would open in the negative x direction.

If it had the form $x^{2}=4py$ , then it would open upward and if $x^{2}=-4py$ , then it opens downward.