Chapter 10.3, Problem 9AYU

For the ellipse $\frac{x^2}{4}+\frac{y^2}{25}=1$, the vertices are the points _______ and _______.

To determine

To fill: The points that represents the vertices of the ellipse $\frac{x^2}{4}+\frac{y^2}{25}=1$.

Answer to Problem 9AYU

Solution:

$\left(0,5\right)$; $\left(0,-5\right)$

Explanation of Solution

Given:

The ellipse $\frac{x^2}{4}+\frac{y^2}{25}=1$.

Formula Used:

For an ellipse $\frac{x^2}{b²}+\frac{y^2}{a²}=1$ where $a>b$.

The vertices are $\left(0,a\right), \left(0,-a\right)$.

Calculation:

$\frac{x^2}{4}+\frac{y^2}{25}=1$ is an ellipse with center $\left(h,k\right)=\left(0,0\right)$, and semi axis $a=5$ and $b=2$.

Hence vertices: $\left(0,\pm a\right)=\left(0, \pm 5\right)$.

Vertices: $\left(0,5\right)$; $\left(0,-5\right)$.