Question

The equation of hyperbola whose center is $(0,0)$, one focus is $(5,0)$ and length of transverse axis is $6$ units is

• A. $\frac{x^2}{9}-\frac{y^2}{25}=1$
• B. $\frac{x^2}{16}-\frac{y^2}{9}=1$
• C. $\frac{x^2}{9}-\frac{y^2}{16}=1$
• D. $\frac{x^2}{25}-\frac{y^2}{16}=1$

Answer 1

The correct option is C $\frac{x^2}{9}-\frac{y^2}{16}=1$

Length of transverse axis $=2a=6$
$\Rightarrow a=3$
Distance between focus and center is $ae=5$
$\therefore e=\frac{5}{3}$
$\Rightarrow \frac{x^2}{a^2}-\frac{y^2}{a^2(e^2-1)}=1$
$\Rightarrow \frac{x^2}{9}-\frac{y^2}{9(\frac{25}{9}-1)}=1$
$\Rightarrow \frac{x^2}{9}-\frac{y^2}{16}=1$