Question

Find an equation

for the ellipse whose graph is shown.

Short answer

Hence, the equation of the ellipse is

Step-by-step solution

Step 1. Given information.

Given graph is centered at the origin.

Step 2. Write down the concept.

The value of both h, k are zero.

The given ellipse is a horizontal ellipse as its longer axis lies on the horizontal axis.

In given graph,

The coordinates of the focus are given as (0, 2) that means c = 2, therefore

$2=\sqrt{a^2-2^2}$

$\begin{array}{l}\Rightarrow 4=a^2-4\\ \Rightarrow a^2=8\end{array}$

The distance from the center to the endpoint of the minor axis is given as 2, therefore b = 2.

Putting these values in the standard equation of an ellipse, we get

$\begin{array}{l}\Rightarrow \frac{{\left(x-0\right)}^2}{2^2}+\frac{{\left(y-0\right)}^2}{8}=1\\ \Rightarrow \frac{x^2}{4}+\frac{y^2}{8}=1\end{array}$