Chapter 11.2, Problem 25E

To determine

To determine the equation of an ellipse.

Answer to Problem 25E

The equation of the ellipse will be $\frac{{\text{x}}^2}{2}+\frac{{\text{y}}^2}{8}=1$

Explanation of Solution

Given information:

The following graph is given:

  

Calculation:

The major axis of the ellipse is vertical, so the denominator of ${\text{y}}^{\text{2}}$ is greater.

From the graph, it is seen that $\text{c}=2\text{ and b}=2$ so ${\text{c}}^2=4,{\text{ b}}^2=4{\text{ and a}}^2=4+4=8\text{ or a}=\sqrt{8}$ .

Hence the equation of the ellipse will be $\frac{{\text{x}}^2}{2}+\frac{{\text{y}}^2}{8}=1$