Question

The foci of the ellipse $25x^2+36y^2=225$ are

• A. $(\pm \frac{1}{2}\sqrt{11},0)$
• B. $(\pm \frac{5}{2},0)$
• C. $(0,\pm \frac{1}{2}\sqrt{11})$
• D. $(0,\pm \frac{5}{2})$

Answer 1

The correct option is A $(\pm \frac{1}{2}\sqrt{11},0)$

Given ellipse is, $25x^2+36y^2=225$
$\Rightarrow \frac{x^2}{(3{)}^2}+\frac{y^2}{(5/2{)}^2}=1$
$\Rightarrow a=3,b=\frac{5}{2}\therefore e=\sqrt{1-\frac{b^2}{a^2}}=\frac{\sqrt{11}}{6}$
Therefore, foci of the ellipse are $(\pm ae,0)\equiv (\pm \frac{1}{2}\sqrt{11},0)$