Question

Find the eccentricity of the hyperbola whose latus rectum is half of its transverse axis.

Answer 1

Answer:

Eccentricity,$e=\sqrt{\frac{3}{2}}$

Step-by-step explanation:

Formula used:

Eccentricity of Hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\:$ is

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

Given:

Length of latusrectum= Half Length of transverse axis

That is

$\frac{2b^2}{a}=a\\\\\frac{2b^2}{a^2}=1\\\\\frac{b^2}{a^2}=\frac{1}{2}$

Now,

Eccentricity,

$e=\sqrt{1+\frac{b^2}{a^2}}\\\\e=\sqrt{1+\frac{1}{2}}\\\\e=\sqrt{\frac{3}{2}}$