The equation of the ellipse whose vertices are at $( \pm 5,0)$ and foci at $( \pm 4,0)$ is

• Correct answer
  A

  $\frac{x^2}{25}+\frac{y^2}{9}=1$
• B

  $\frac{x^2}{9}+\frac{y^2}{25}=1$
• C

  $\frac{x^2}{16}+\frac{y^2}{25}=1$
• D

  $\frac{x^2}{25}+\frac{y^2}{16}=1$

Solution

$\begin{aligned} & a=5 \text { and } a e=4 \\ & e=\frac{4}{5}\end{aligned}$ $\begin{aligned} & e^2=1-\frac{b^2}{a^2} \\ & \frac{16}{25}=1-\frac{b^2}{25}\end{aligned}$ $\begin{aligned} & \Rightarrow \frac{b^2}{25}=\frac{9}{25} \quad \Rightarrow b^2=9 \\ & \frac{x^2}{25}+\frac{y^2}{9}=1\end{aligned}$

Hence, the correct answer is option: 'A'.