Question

The distance between the foci is $4\sqrt{13}$ and the length of conjugate axis is $8$ then then eccentricity of the hyperbola is

• A. $\frac{\sqrt{13}}{3}$
• B. $\frac{\sqrt{13}}{5}$
• C. $\frac{\sqrt{11}}{3}$
• D. none

Answer 1

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

solution-

Distance between foci = $2ae=4\sqrt{13}$

conjugate axis $=2b=8$

$b=4.$

$ae=2\sqrt{13}$

$a\sqrt{1+\frac{b^2}{a^2}}=2\sqrt{13}$

$a^2+16=52$

$a^2=36.$

$e=\sqrt{\frac{1+b^2}{a^2}}=\sqrt{\frac{1+16}{36}}=\frac{2\sqrt{13}}{6}=\frac{\sqrt{13}}{3}$

$A$ is correct