Chapter 9.2, Problem 13E

To determine

Tofind:The standard equation of the ellipse using the characteristics given in the below graph.

  

Answer to Problem 13E

The equation of the ellipse is $\frac{x^2}{2^2}+\frac{y^2}{4^2}=1$ .

Explanation of Solution

Given information:

The graph of the ellipse is shown below.

  

Calculation:

In the give graph, the major axis of the given ellipse is vertical. So, the general equation of the ellipse is $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ .

From the graph, the values are $a=4$ and $b=2$ .

Substitute these values in the general equation of the ellipse.

  $\begin{array}{l}\frac{x^2}{b^2}+\frac{y^2}{a^2}=1\\ \frac{x^2}{2^2}+\frac{y^2}{4^2}=1\end{array}$

Therefore, the equation of the ellipse is $\frac{x^2}{2^2}+\frac{y^2}{4^2}=1$ .