Question

A focus of the hyperbola $25x^2-36y^2=225$ is

• A. $(\sqrt{61},0)$
• B. $(\frac{1}{2}\sqrt{61},0)$
• C. $(-\sqrt{61},0)$
• D. $(-\frac{1}{2}\sqrt{61},0)$

Answer 1

Answer: (B), (D)

$(-\frac{1}{2}\sqrt{61},0)$
$(\frac{1}{2}\sqrt{61},0)$

The equation of the given hyperbola in standard form is

$\frac{x^2}{9}-\frac{y^2}{25/4}=1$

The focii of a hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ are $(\pm ae,0)$ where $e^2=1+\frac{b^2}{a^2}$
Here, $a^2=9$ and $b^2=\frac{25}{4}$
So, $e^2=\frac{61}{36}$
The coordinates of the focii are $(\frac{\sqrt{61}}{2},0)$ and $(-\frac{\sqrt{61}}{2},0)$