Question

Write the equation of the ellipse with a vertex at (0,-9), a co-vertex at (8,0), and center at the orgin.

Answer 1

If a vertex is (0,-9), the other vertex is (0,9) so we see that the major axis is vertical which means that a^2 is under the y term and b^2 is under the x term. Also we know that a = 9 so a^2=81. b=8 so b^2=64 so the equation is:

Answer 2

\[\frac{x^2}{64}+\frac{y^2}{81}=1\]