Question

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

• A. $\frac{x^2}{25}+\frac{y^2}{16}=1$
• B. $9x^2+25y^2=225$
• C. $\frac{x^2}{9}+\frac{y^2}{25}=1$
• D. $4x^2+5y^2=20$

Answer 1

Answer: (B)

$9x^2+25y^2=225$

The vertices and foci of an ellipse are $(\pm 5,0)$ and $(\pm 4,0)$ respectively.
$\therefore a=5$ and $ae=4$
$\Rightarrow e=\frac{4}{5}$
We know that,
$e=\sqrt{1-\frac{b^2}{a^2}}$
$\Rightarrow \frac{16}{25}=1-\frac{b^2}{25}\Rightarrow b^2=9$
Hence, equation of an ellipse is
$\frac{x^2}{25}+\frac{y^2}{9}=1\Rightarrow 9x^2+25y^2=225$