# How do you find the equation of an ellipse with foci (+-2,0) and major axis of length 8?

Dec 17, 2016

${x}^{2} / 16 + {y}^{2} / 12 = 1$. Graph is inserted.

#### Explanation:

The line of foci is the major axis and, here, it is the x-axis y = 0.

The center is the midpoint of the join of theci, and so, it is the origin

(0, 0 ).

The major axis 2a = 8. So, a = 4.

THe distance between the foci = 2a X (eccentricity) = 2ae = 6e = 4. So, e = 1/2.

The semi minor axis $b = a a \sqrt{1 - {e}^{2}} = 4 \sqrt{1 - \frac{1}{4}} = 2 \sqrt{3}$.

Now, the equation is

${x}^{2} / {a}^{2} + {y}^{2} / {b}^{2} = {x}^{2} / 16 + {y}^{2} / 12 = 1$

The graph is inserted.

graph{x^2/16+y^2/12-1=0 [-10, 10, -5, 5]}