# How do you write an equation of an ellipse in standard form given foci = (0,-3) and (0,3);length of major axis: 10?

Mar 20, 2016

${x}^{2} / 25 + {y}^{2} / 16 = 1$.

#### Explanation:

Foci are on the major axis. So, the major axis is x-axis . Center is the midpoint of the the line joining the foci, (0, 0).
So, the equation of the ellipse is
${x}^{22} / \left({a}^{2}\right) + {y}^{2} / \left({b}^{2}\right) = 1$,
where a and b are the lengths of semi-major and semi-minor axes.

The eccentricity e = (distance between the foci)$/$(the length of the major axis) = (2ae)/(2a)=3/5.

The semi-minor axis b = a$\sqrt{1 - {e}^{2}}$ = 5$\sqrt{1 - \frac{9}{25}}$ = 4
Answer: ${x}^{2} / 25 + {y}^{2} / 16 = 1$.