Question

The eccentricity of a rectangular hyperbola is

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

Hint:

In a rectangular hyperbola, the transverse and conjugate axes are equal.

Answer 1

The Correct Option is D

Step 1: Writing the standard form.
A rectangular hyperbola has the equation \[ \frac{x^2}{a^2}-\frac{y^2}{a^2}=1 \]
Step 2: Finding eccentricity.
For a hyperbola, \[ e=\sqrt{1+\frac{b^2}{a^2}} \] Here $a=b$.
Step 3: Substituting values.
\[ e=\sqrt{1+1}=\sqrt{2} \]
Step 4: Conclusion.
The eccentricity of a rectangular hyperbola is $\sqrt{2}$.