Question

What is the equation of the ellipse with foci (-10, 0), (10, 0) and co-vertices (0, -3), (0, 3)?

Answer 1

The focii of an ellipse are given by (-ae,0) and (ae,0), so you know that the value of ae is 10.
Similarly the co vertices are (b,0) and (-b,0). So the value of b is 3.
Now use the equation
\[e = \sqrt{1-\frac{ b ^{2} }{ a ^{2} }}\]
to find the value of a. Then the equation of the ellipse would be:
\[\frac{ x ^{2} }{ a ^{2} } + \frac{ y ^{2} }{ b ^{2} } = 1\]