Foci of an Ellipse

I read an article on local math whizzes who visited President Obama in the Oval Office.

They asked him "where are the foci of the Oval Office?"

It turns out, finding the foci of an ellipse is another extension of the Pythagorean theorem. As seen below.

Notice the 'a' 'b' and 'c ' here are not as they usually are in the Pythagorean theorem. "C" is a leg of the triangle here, not the hypotenuse. Otherwise, the formula they give here is just to find the leg of a triangle (here called "C" and falling on the X-axis), using the co-vertex and origin to make a right triangle.

Also notice that in this example, they use a 3-4-5 Triangle, which is a Pythagorean Triple.

If you want to read some academic history on the further wonders of Pythagoras, you can stretch your mind here.