# How to find an equation of an ellipse?

Find the equation of an ellipse with the following.

$$Center: (0,0)\ Focus: (3,0)\ Vertex: (-4,0)$$

`a`

is the distance from the origin of the ellipse
`c`

is the distance from the origin to the foci
$$ a = 4 $$
$$ c = 3 $$
$$ foci = (3,0), (-3,0) $$
$${b}^{2} = {a}^{2}-{c}^{2}$$
$${b}^{2} = {4}^{2}-{3}^{2}$$
$${b}^{2} = 16-9$$
$${b}^{2} = 7$$

Remember the standard form of an ellipse?

$$\frac { { x }^{ 2 } }{16} +\frac { { y }^{ 2 } }{ 7 } =1$$