Homework Help: Parabola conical whatever equations

1. Jun 5, 2006

runicle

I am dazed and confused how does 2x^2=y end up being directrix y=-1/8?

2. Jun 5, 2006

runicle

I forgot the steps on how to do this.

3. Jun 5, 2006

Andrew Mason

Putting the parabola into form $x^2 = 4py$ where p is the focus, will give you the location of the focus, p. Since the points on the parabola are equidistant form the directrix and focus, that should enable you to find the equation of that line.

AM

4. Jun 5, 2006

runicle

I don't see the math in it though...
$x^2 = 4py$
$x/4^2 = py$
making $x/4^2 = p$
is it something like that?

5. Jun 6, 2006

Andrew Mason

No. $2x^2 = y$ so $x^2 = \frac{1}{2}y$. In the form $x^2 = 4py$ 4p = 1/2 and p = 1/8. So the focus is (0,1/8). Since the vertex is (0,0) which is equidistant from the focus and the directrix, the directrix is the horizontal line passing through (0,-1/8) ie. y = -1/8

AM