# How do you write an equation of an ellipse in standard form given center (-1, 3) vertex (3,3) and minor axis of length 2?

Jan 26, 2016

${\left(x + 1\right)}^{2} / 16 + {\left(y - 3\right)}^{2} / 4 = 1$

#### Explanation:

The standard form for an ellipse is
(x-h)^"/a^2 +(y-k)^2/b^2 = 1
where $\left(h , k\right)$ is the centre of the ellipse, $a$ is the distance from the centre to the vertices and $c$ is the distance from the centre to the foci. $b$ is the minor axis.

${b}^{2} + {c}^{2} = {a}^{2}$

In this example $a = 3 - \left(- 1\right) = 4$ (The difference if the $x$ coordinates of the centre and the vertex.)

The equations is ${\left(x + 1\right)}^{2} / 16 + {\left(y - 3\right)}^{2} / 4 = 1$