Question

The eccentricity of the hyperbola $4x^2-9y^2-8x=32$ is

• A. $\frac{\sqrt{5}}{3}$
• B. $\frac{\sqrt{13}}{3}$
• C. $\frac{4}{3}$
• D. $\frac{3}{2}$

Answer 1

The correct option is B $\frac{\sqrt{13}}{3}$

$4x^2-9y^2-8x=32$
$\Rightarrow 4(x^2-2x)-9y^2=32$
$\Rightarrow 4(x^2-2x+1)-9y^2=32+4=36$
$\Rightarrow \frac{(x-1{)}^2}{9}-\frac{y^2}{4}=1$
$\Rightarrow a^2=9,b^2=4$
$\therefore e=\sqrt{1+\frac{b^2}{a^2}}=\frac{\sqrt{13}}{3}$
Hence, option 'B' is correct.