Question

Find an equation

for the ellipse that satisfies the given conditions.

Foci: $(\pm 4,0)$, vertices: $(\pm 5,0)$

Short answer

Hence, the equation of ellipse is .

Step-by-step solution

Step 1. Given information.

Given the Focus and vertices of ellipse.

Foci:$(\pm 4,0)$,vertices:$(\pm 5,0)$

Step 2. Write down the concept.

Comparing the given equation with the standard equation,

$\begin{array}{l}\Rightarrow a=5\\ \Rightarrow c=4\\ \Rightarrow b=\sqrt{25-16}\\ \Rightarrow b=\sqrt{9}\\ \Rightarrow b=3\end{array}$

Hence,

the equation of ellipse is .