Question

Eccentricity of hyperbola$\frac{x^2}{k}-\frac{y^2}{k}=1$

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

Answer 1

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

$Standardhyperbola:$

$\frac{x^2}{k}-\frac{y^2}{k}=1$

$Now,\frac{{\left(x-h\right)}^2}{a^2}-\frac{{\left(y-k\right)}^2}{b^2}=1$

$ThereforeHyperbolapropertiesare(h,k)=\left(0,0\right),a=\sqrt{k},b=\sqrt{k}$

$=\frac{\sqrt{{\left(\sqrt{k}\right)}^2+{\left(\sqrt{k}\right)}^2}}{\sqrt{k}}$

$=\sqrt{2}Hence,theoptionCisthecorrectanswer$