Chapter 9.2, Problem 14E

To determine

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

  

Answer to Problem 14E

The equation of the ellipse is $\frac{x^2}{2^2}+\frac{4y^2}{{\left(3\right)}^2}=1$ .

Explanation of Solution

Given information:

The graph of the ellipse is shown below.

  

Calculation:

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

From the graph, the values are $a=2$ and $b=\frac{3}{2}$ .

Substitute these values in the general equation of the ellipse.

  $\begin{array}{l}\frac{x^2}{b^2}+\frac{y^2}{a^2}=1\\ \frac{x^2}{2^2}+\frac{y^2}{{\left(\frac{3}{2}\right)}^2}=1\end{array}$

Therefore, the equation of the ellipse is $\frac{x^2}{2^2}+\frac{y^2}{{\left(\frac{3}{2}\right)}^2}=1$ .