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Can you help me out with the next problem. I have an ellipse based on a width and a height. Is there any way you can find out where the focal points are?

I need this information because I need to know how long each radius is.

Thanks in advance.

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2 Answers

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The width of an ellipse is twice its semi-minor axis, $b$, and the length is twice its semi-major axis, $a$.

The distance from the focus, $F$, to the end of the semi-minor axis, $B$, is the same as the distance from the center of the ellipse, $O$, to the end of the semi-major axis, $A$.

$\hspace{3.5cm}$enter image description here

The Pythagorean Theorem says that the distance from $O$ to $F$ is $\sqrt{a^2-b^2}$

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Are you looking for this formula?

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It might be a good idea to include the relevant parts of that link here; links can break, and in particular, Wikipedia may change so that the internal link may no longer be valid. – Arkamis Nov 5 '12 at 15:50
The thing is I don't have the minor and major radius. So I can't use the formula. – Tijmen Nov 5 '12 at 16:39
Excuse me, what are the wigth and the height then? – user983302 Nov 5 '12 at 16:55
For example. You've got an ellipse in a rectangle with width s and height p. How can I express the place of the foci in s and p? – Tijmen Nov 5 '12 at 17:05
If ellipse and rectangle have four contact points: translate and maybe rotate an ellipse to situate its center in $(0,0)$, and then $a = p / 2$, $b = s / 2$ (or vice versa). If you need positions of foci as vectors, make inverse translation and rotation. If there are less than four contact points, there are infinity of solutions. – user983302 Nov 5 '12 at 17:17

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