Question

The equation of the hyperbola whose vertices are $(\pm 2,0)$ and foci are $(\pm 3,0)$ is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$ Sum of $a^2$ and $b^2$ is

• A. 5
• B. 4
• C. 9
• D. 1

Answer 1

Answer: (C)

Since the foci are on $x$-axis, the equation of the
hyperbola is of the form $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
Given: vertices are $(\pm 2,0),a=2$
Also, since foci are $(\pm 3,0),c=3$ and
$b^2=c^2-a^2=9-4=5$
$\therefore$ the equation of the hyperbola is : $\frac{x^2}{4}-\frac{y^2}{5}=1$