# A question about the distance from the center to the foci of a hyperbola.

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 ?

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