Question

The eccentricity of the hyperbola \[x^{2}-y^{2}=25\] is______.

Options

• \[\sqrt{2}\]

• \[\frac{1}{\sqrt{2}}\]

• 2

• \[1+\sqrt{2}\]

Answer 1

The eccentricity of the hyperbola \[x^{2}-y^{2}=25\] is \[\sqrt{2}\].

Explanation:

Rewrite in standard form:

              \[x^2-y^2=25\Rightarrow\frac{x^2}{25}-\frac{y^2}{25}=1\]

So \[a^2=25,b^2=25.\]

Eccentricity of hyperbola:

              \[e=\sqrt{1+\frac{b^2}{a^2}}=\sqrt{1+\frac{25}{25}}=\sqrt{1+1}=\sqrt{2}\]