Chapter 11.2, Problem 36E

To determine

To determine the equation of the ellipse.

Answer to Problem 36E

The equation of the ellipse is $\frac{{\text{x}}^2}{9}+\frac{{\text{y}}^2}{4}=1$ .

Explanation of Solution

Given information:

The given conditions are:

Length of major axis: $6$

Length of minor axis: $4$

Foci is on x-axis

Formula used:

The following formula is used:

  $\begin{array}{l}\text{Length of major axis}=\text{2a}\\ \text{Length of minor axis}=\text{2b}\end{array}$

Calculation:

The foci lies on x-axis, so the ellipse has a major horizontal axis and ${\text{a}}^2$ is the denominator of ${\text{x}}^2$

The value of $\text{a and b}$ can be calculated by:

  $\begin{array}{l}\text{Length of major axis}=6\\ \text{2a}=6\\ \text{a}=3\\ \text{Length of minor axis}=4\\ \text{2b}=4\\ \text{b}=2\end{array}$

The equation can be obtained by:

  $\begin{array}{l}\frac{{\text{x}}^2}{{\text{a}}^2}+\frac{{\text{y}}^2}{{\text{b}}^2}=1\\ \text{or }\frac{{\text{x}}^2}{3^2}+\frac{{\text{y}}^2}{2^2}=1\\ \text{or }\frac{{\text{x}}^2}{9}+\frac{{\text{y}}^2}{4}=1\end{array}$

Hence, the equation of the ellipse is $\frac{{\text{x}}^2}{9}+\frac{{\text{y}}^2}{4}=1$ .