Question

The equation of the hyperbola whose foci are $(-2,0)$ and $(2,0)$ and eccentricity is $2$ is given by:

• A. $x^2-3y^2=3$
• B. $-x^2+3y^2=3$
• C. $3x^2-y^2=3$
• D. $-3x^2+y^2=3$

Answer 1

The correct option is C $3x^2-y^2=3$

Let the equation of the hyperbola is

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

where $2ae=4$ and $e=2\Rightarrow a=1$

$a^2{e}^2=a^2+b^2\Rightarrow 4=1+b^2$

$b^2=3$

$\therefore$ equation of hyperbola is $\frac{x^2}{1}-\frac{y^2}{3}=1$

$3x^2-y^2-3=0$