NDA 2025 Maths · Mathematics · Conic Sections · easy

The eccentricity of the rectangular hyperbola x^2-y^2=a^2 is

Single correct option

The eccentricity of the rectangular hyperbola

x^2-y^2=a^2

Show answer and solution

Answer: (C) $\sqrt2$

Here the transverse and conjugate semi-axes are both

a

, so

b^2=a^2

and

e=\sqrt{1+\frac{b^2}{a^2}}=\sqrt2

. The value

\frac1{\sqrt2}

is less than

1

, which is impossible for a hyperbola,

1

is the eccentricity of a parabola, and

2

forgets the square root.

Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake