Q93 / 160 · AP EAMCET 2022 (07 Jul Shift 2) · Mathematics
The foci of the ellipse $9 x^2+25 y^2=225$ are
- Correct answerA$( \pm 4,0)$
- B$\left( \pm \frac{4}{5}, 0\right)$
- C$\left( \pm \frac{12}{5}, 0\right)$
- D$\left( \pm \frac{2}{5}, 0\right)$
Solution
Ellipse is $9 x^2+25 y^2=225$
$$
\begin{aligned}
& \Rightarrow \frac{x^2}{25}+\frac{y^2}{9}=1, a=5, b=3 \\
& \therefore e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{9}{25}}=\frac{4}{5}
\end{aligned}
$$
$\therefore$ Foci are $( \pm a e, 0) \equiv( \pm 4,0)$
Hence, the correct answer is option: 'A'.