# Ellipse Question

• Oct 19th 2009, 12:06 PM
Kevlar
Ellipse Question
Find the co-ordinates of the centre and foci of the ellipse with equation
$\displaystyle 25x^2+16y^2-100x-256y+724=0$
What are the coordinated of its verices and the eqns of the directrices?

I've managed to manipulate the eqn to this form

$\displaystyle \frac{(x-2)^2}{16}+\frac{(y-8)^2}{25}=1$

Therefore got the centre as (2,8).

I did vertex, directrix and foci for parabolas but not for an ellipse what are the formula? :s i've tried looking them up on the web but it's all confusing. So far i think

Directrix=$\displaystyle +-\frac{a^2}{c}$

Can someone help me out with just this one ? >.< got a whole load more of em to work through that are similar just im stuck at the first hurdle haha
• Oct 19th 2009, 12:24 PM
earboth
Quote:

Originally Posted by Kevlar
Find the co-ordinates of the centre and foci of the ellipse with equation
$\displaystyle 25x^2+16y^2-100x-256y+724=0$
What are the coordinated of its verices and the eqns of the directrices?

I've managed to manipulate the eqn to this form

$\displaystyle \frac{(x-2)^2}{16}+\frac{(y-8)^2}{25}=1$

Therefore got the centre as (2,8).

I did vertex, directrix and foci for parabolas but not for an ellipse what are the formula? :s i've tried looking them up on the web but it's all confusing. So far i think

Directrix=$\displaystyle +-\frac{a^2}{c}$

Can someone help me out with just this one ? >.< got a whole load more of em to work through that are similar just im stuck at the first hurdle haha

Have a look here: Ellipse -- from Wolfram MathWorld

(You have to scroll down a little bit!)