Question

The length of latus rectum of the hyperbola $4x^2-9y^2-16x-54y-101=0$ is

• A. $\frac{8}{5}$
• B. $\frac{8}{7}$
• C. $\frac{8}{9}$
• D. $\frac{8}{3}$

Answer 1

The correct option is D $\frac{8}{3}$

$4x^2-9y^2-16x-54y-101=0$
$\Rightarrow 4(x^2-4x)-9(y^2+6y)=101$
$\Rightarrow 4(x^2-4x+4)-9(y^2+6y+9)=101+16-81=36$
$\Rightarrow \frac{(x-2{)}^2}{3^2}-\frac{(y+3{)}^2}{2^2}=1$
$\Rightarrow a=3,b=2$
Thus length of latus rectum of the given hyperbola is $=\frac{2b^2}{a}=\frac{8}{3}$