Chapter 9, Problem 45SGR

To determine

To find: The equation to the model of the garden.

Answer to Problem 45SGR

The equation to the model of the garden is $\frac{x^2}{64}+\frac{y^2}{25}=1$ .

Explanation of Solution

Given information:

Major axis is $16\text{ft}$ long and the minor axis is $10\text{ ft}$ long.

Calculation:

Consider a garden that is shaped like an ellipse. The major axis is $16\text{ ft}$ long and the minor axis is $10\text{ ft}$ long.

Length of long axis will be equal to the value of 2a. So,

  $\begin{array}{c}2a=16\\ a=8\end{array}$

Length of short axis will be equal to the value of 2b. So,

  $\begin{array}{c}2b=10\\ b=5\end{array}$

Use the equation of a horizontal ellipse with center at origin.

  $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Substitute $a=8$ and $b=5$ .The equation that models the garden will be,

  $\begin{array}{l}\frac{x^2}{8^2}+\frac{y^2}{5^2}=1\\ \frac{x^2}{64}+\frac{y^2}{25}=1\end{array}$

Therefore, the equation to the model of the garden is $\frac{x^2}{64}+\frac{y^2}{25}=1$ .