Question

The distance between the foci of the hyperbola $x^2-3y^2-4x-6y-11=0$ is

• A. 4
• B. 6
• C. 8
• D. 10

Answer 1

Answer: (C)

$x^2-3y^2-4x-6y-11=0$
$\Rightarrow \left(x^2-4x\right)-3\left(y^2+2y\right)=11$
$\Rightarrow \left(x^2-4x+4\right)-3\left(y^2+2y+1\right)=11+1$
$\Rightarrow \frac{(x-2{)}^2}{12}-\frac{(y+1{)}^2}{4}=1$
$\Rightarrow a^2=12,b^2=4$
$\therefore e=\sqrt{1+\frac{b^2}{a^2}}=\frac{2}{\sqrt{3}}$
Therefore distance between focii is
$=2ae=2\times 2\sqrt{3}\times \frac{2}{\sqrt{3}}$
$=8$