# How do you find the equation in standard form of an ellipse that passes through the given points: (-8, 0), (8, 0), (0, -4), (0, 4)?

Dec 21, 2016

The equation is ${x}^{2} / 64 + {y}^{2} / 16 = 1$

#### Explanation:

We use the equation the standard ellipse as the center is $\left(0 , 0\right)$

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

Let's take the vertex $\left(8 , 0\right)$, then

$\frac{64}{a} ^ 2 + 0 = 1$, $\implies$, $a = 8$

Let's take the vertex $\left(0 , 4\right)$, then

$0 + \frac{16}{b} ^ 2 = 1$, $\implies$, $b = 4$

The equation of the ellipse is

${x}^{2} / 64 + {y}^{2} / 16 = 1$

graph{x^2/64+y^2/16=1 [-12.66, 12.65, -6.33, 6.33]}