Question

What is the eccentricity of rectangular hyperbola?

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $\sqrt{5}$
• D. $\sqrt{6}$

Answer 1

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

Rectangular hyperbola is a hyperbola for which the asymptotes are perpendicular, also called an equilateral hyperbola or right hyperbola. This occurs when the si-major and semi-major axes are equal.

So, $a=b$

Since the eccentricity of the hyperbola is given by,

$e=\frac{(a^2+b^2{)}^{1/2}}{a}$

$\Rightarrow e=\frac{(2a^2{)}^{1/2}}{a}$

$\Rightarrow e=\frac{\sqrt{2}a}{a}$

Hence, $e=\sqrt{2}$