Question

The vertices of a hyperbola are (2, 0), (–2, 0) and the foci are (3, 0), (–3, 0). The equation of the hyperbola is

• A. $\frac{x^2}{5}-\frac{y^2}{4}=1$
• B. $\frac{x^2}{4}-\frac{y^2}{5}=1$
• C. $\frac{x^2}{5}-\frac{y^2}{2}=1$
• D. $\frac{x^2}{2}-\frac{y^2}{5}=1$

Answer 1

The correct option is B

$\frac{x^2}{4}-\frac{y^2}{5}=1$

$Centre=(0,0),a=2,ae=3\Rightarrow e=\frac{3}{2}$

$b^2=a^2(e^2-1)=a^2{e}^2-a^2=9-4=5$

equation of the hyperbola is $\frac{x^2}{4}-\frac{y^2}{5}=1$