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When it comes to an ellipse, I know that an ellipse with major axis $2a$ and minor axis $2b$ and a distance from the center to the foci $c$ has a relationship $b^2+c^2=a^2$.

This can be shown by using the definition of the focal radii and just pick the covertex to come up with this equality.

A similar situation with a hyperbola gives us $a^2+b^2=c^2$, but I don't know why this is true.

I am trying to convince my students with basic precalc material, can someone help me out ?

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  • $\begingroup$ Have you looked at Wolfram's explanation? $\endgroup$ – Doctor Dan Sep 10 '13 at 18:38
  • $\begingroup$ No I have not. Thanks for the referral ! $\endgroup$ – hyg17 Sep 12 '13 at 6:11

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