[Math] Foci of Ellipse – given: Width and Height

analytic geometryconic sections

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.

Best Answer

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, $A$.

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

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