Chapter 10.3, Problem 75AYU

To determine

To find: The width of the ellipse which is 10 feet from the vertex.

Answer to Problem 75AYU

  $24.65$

Explanation of Solution

Given:A racetrack which is 100 feet long and 50 feet wide in the shape of ellipse.

  

It is given that aracetrack which is 100 feet long and 50 feet wide in the shape of ellipse.

  

  $\begin{array}{l}h=0\\ k=0\\ a=60\\ b=25\end{array}$

  $\begin{array}{l}\frac{x^2}{{60}^2}+\frac{y^2}{{25}^2}=1\\ \frac{x^2}{3600}+\frac{y^2}{625}=1\\ \text{when }x=10\\ \frac{{10}^2}{3600}+\frac{y^2}{625}=1\\ \frac{100}{3600}+\frac{y^2}{625}=1\\ y=24.65\end{array}$

  $\begin{array}{l}\text{when }x=30\\ \frac{{30}^2}{3600}+\frac{y^2}{625}=1\\ \frac{900}{3600}+\frac{y^2}{625}=1\\ y=21.65\end{array}$

  $\begin{array}{l}\text{when }x=50\\ \frac{{50}^2}{3600}+\frac{y^2}{625}=1\\ \frac{2500}{3600}+\frac{y^2}{625}=1\\ y=13.82\end{array}$

Hence, the width is $24.65$