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

Putting these values (-1 , 2) in the standard equation of an ellipse, we get

$\begin{array}{l}\Rightarrow \frac{{\left(-1-0\right)}^2}{2^2}+\frac{{\left(2-0\right)}^2}{a^2}=1\\ \Rightarrow \frac{1}{4}+\frac{4}{a^2}=1\\ \Rightarrow \frac{4}{a^2}=1-\frac{1}{4}\\ \Rightarrow \frac{4}{a^2}=\frac{3}{4}\\ \Rightarrow a^2=\frac{16}{3}\end{array}$

Using this value of $a^2$in the standard equation we get

$\begin{array}{l}\Rightarrow \frac{x^2}{2^2}+\frac{y^2}{16/3}=1\\ \Rightarrow \frac{x^2}{4}+\frac{3y^2}{16}=1\end{array}$