Question

If $e_{1}and{e}_2$ are the eccentricities of a hyperbola and its conjugate respectively, Then $e_1^{-2}+e_2^{-2}=1$.

• A. True
• B. False

Answer 1

The correct option is A

True

We have to remember the relation between the eccentricities of both the hyperbolas with their respectives axes lengths.

Here,

$e_1^2=1+\frac{b^2}{a}=\frac{a^2+b^2}{a^2}$

And corresponding parameter for its conjugate hyperbola can be obtained by interchanging the position of a and b. if$e_2$ is the eccentricity of the conjugate hyperbola,Then,

$e_2^2=1+\frac{a^2}{b^2}=\frac{a^2+b^2}{a^2}$