Question

A rectangular hyperbola is represented by the equation $x^2-y^2=2^2$, calculate the eccentricity value.

• A. $\sqrt{2}+1$
• B. $2$
• C. $\sqrt{2}$
• D. $\sqrt{3}$

Answer 1

The correct option is C $\sqrt{2}$

Given: Rectangular hyperbola $x^2-y^2=2^2$

To Find: Eccentricity

We know that, the eccentricity of a standard hyperbola is calculated using the equation,
$e=\sqrt{1+\frac{b^2}{a^2}}$

Also, in a rectangular hyperbola, $a=b$.

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

$\Rightarrow e=\sqrt{1+1}=\sqrt{2}$

This result implies that the eccentricity of a rectangular hyperbola remains $\sqrt{2}$ irrespective of the rectangular hyperbola equation.