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

The correct option is C $8$

Given, equation of hyperbola is
$x^2-3y^2-4x-6y-11=0$
$\Rightarrow (x^2-4x+4)-3(y^2+2y+1)-11=4-3$
$\Rightarrow {(x-2)}^2-3{(y+1)}^2=12$
$\Rightarrow \frac{{(x-2)}^2}{12}-\frac{{(y+1)}^2}{4}=1$
Now, $e=\sqrt{1+\frac{4}{12}}=\frac{2}{\sqrt{3}}$
$\therefore$ Distance between foci $=2ae=2\times \sqrt{12}\times \frac{2}{\sqrt{3}}=8$