# Equation of ellipse from directrix and focus

• Jul 5th 2012, 07:35 PM
daigo
Equation of ellipse from directrix and focus
Quote:

Find the equation of an ellipse with a directrix y = -2 and a focus at the origin.
I'm trying to find the polar equation first, and I learned this today but I forgot a lot of it and we're not allowed to take notes in class (professor says it helps to learn better) so I'm trying to look it up online but it's not much help because I can't find any elementary lessons on polar equations.

Anyway, I think the formula is

$\displaystyle r = \frac{pe}{1 \pm sin\theta }$

because of the position of the directrix, I know the ellipse is elongated along the y-axis. For this particular position given in the problem, I know it's a negative sign in the denominator (for the plus-minus symbol).

I know 'e' is eccentricity and to find that I need the center point but I forgot how to get it. I also need the vertex but I forgot how to find that too. But I know the lower vertex is between that given focus and directrix.

So far I have:

$\displaystyle r = \frac{(2)e}{1 - sin\theta }$

First step: how do I find the length of the major axes or a vertex?