Chapter A5.1, Problem 20E

To determine

To find: the ellipse’s standard-form equation

Answer to Problem 20E

The ellipse’s standard-form equation is:

  $\frac{x^2}{9}+\frac{y^2}{25}=1$

Explanation of Solution

Given:

  $\begin{array}{l}Foci:\left(0,\pm 4\right)\\ Vertices:\left(0,\pm 5\right)\end{array}$

Calculation:

Given:

  $\begin{array}{l}Foci:\left(0,\pm 4\right)\Rightarrow \left(0,\pm c\right)\\ Vertices:\left(0,\pm 5\right)\Rightarrow \left(0,\pm a\right)\end{array}$

On comparing, we get

  $\begin{array}{l}c=4\\ a=5\\ b=\sqrt{a^2-c^2}=3\end{array}$

Therefore equation is:

  $\frac{x^2}{9}+\frac{y^2}{25}=1$

Conclusion:

The ellipse’s standard-form equation is:

  $\frac{x^2}{9}+\frac{y^2}{25}=1$