The focal length is found by equating the general expression for y

`y=x^2/(4p)`

and our particular example:

`y=x^2/2`

So we have:

`x^2/(4p)=x^2/2`

This gives `p = 0.5`.

So the focus will be at `(0, 0.5)` and the directrix is the line `y = -0.5`.

Our curve is as follows:

Parabola showing focus and directrix

Note: Even though the sides look as though they become straight as x increases, in fact they do not. The sides of a parabola just get steeper and steeper (but are never vertical, either).

Easy to understand math videos:
MathTutorDVD.com