Question

Find an equation

for the ellipse that satisfies the given conditions.

Foci: $(0,\pm 2)$, vertices: $(0,\pm 3)$

Short answer

Hence, the equation of ellipse is .

Step-by-step solution

Step 1. Given information.

Given the Focus and vertices of ellipse.

Foci:$(0,\pm 2)$,vertices:$(0,\pm 3)$

Step 2. Write down the concept.

Comparing the given equation with the standard equation,

$\begin{array}{l}\Rightarrow b=3\\ \Rightarrow c=2\\ \Rightarrow 2^2=3^2-a^2\\ \Rightarrow 4=9-a^2\\ \Rightarrow a^2=9-4\\ \Rightarrow a^2=5\end{array}$

Hence,

the equation of ellipse is $〈\frac{x^2}{5}+\frac{y^2}{9}=1〉$.