The foci of the ellipse $9 x^2+25 y^2=225$ are

The foci of the ellipse $9 x^2+25 y^2=225$ are
  1. $( \pm 4,0)$
  2. $\left( \pm \frac{4}{5}, 0\right)$
  3. $\left( \pm \frac{12}{5}, 0\right)$
  4. $\left( \pm \frac{2}{5}, 0\right)$

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 $( \pm a e, 0) \equiv( \pm 4,0)$

Asked in: AP EAMCET 2022 (07 Jul Shift 2)

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