Chapter 9.2, Problem 9E

To determine

To match: The equation $\frac{x^2}{4}+\frac{y^2}{9}=1$ with the given graphs.

  

Answer to Problem 9E

The graph of ellipse equation $\frac{x^2}{4}+\frac{y^2}{9}=1$ is graph $\left(b\right)$ .

Explanation of Solution

Given information:

Given equation $\frac{x^2}{4}+\frac{y^2}{9}=1$ and its one of the graph among the four graphs

  

Calculation:

The equation of the ellipse is $\frac{x^2}{4}+\frac{y^2}{9}=1$ with center $\left(0,0\right)$ as $h=0$ and $k=0$ .

Substitute $0$ for $x$ in the equation of the ellipse.

  $\begin{array}{c}\frac{x^2}{4}+\frac{y^2}{9}=1\\ \frac{0^2}{4}+\frac{y^2}{9}=1\\ y^2=9\\ y=\pm 3\end{array}$

The ellipse passes through the points $\left(0,\pm 3\right)$ .

Therefore, the graph of ellipse equation $\frac{x^2}{4}+\frac{y^2}{9}=1$ is graph $\left(b\right)$ .