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  4. Eccentricity of the curve x2-y2=a2 is equal to

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Q. Eccentricity of the curve $ {{x}^{2}}-{{y}^{2}}={{a}^{2}} $ is equal to

J & K CETJ & K CET 2003

Solution:

Given equation of curve can be rewritten as
$ \frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{a}^{2}}}=1 $
$ \therefore $ $ e=\sqrt{1+\frac{{{b}^{2}}}{{{a}^{2}}}}=\sqrt{1+\frac{{{a}^{2}}}{{{a}^{2}}}} $
$ \Rightarrow $ $ e=\sqrt{2} $