Find the eccentricity of the hyperbola.
-$$x ^ { 2 } - 2 y ^ { 2 } = 6$$
A) $\sqrt { 2 }$
B) $\sqrt { 6 }$
C) $\frac { \sqrt { 6 } } { 2 }$
D) $\frac { \sqrt { 2 } } { 2 }$

Question

Quizplus · Accepted Answer

We can rewrite the equation as $\frac{x^2}{6} - \frac{y^2}{3} = 1$. 
Therefore, $a^2=6$ and $b^2=3$, and we can find the eccentricity using the formula $e=\sqrt{a^2+b^2}/a$. 
Plugging in our values, we get $e=\sqrt{6+3}/\sqrt{6}= \frac{\sqrt{6}}{2}$. Therefore, the correct answer is (C).

Find the Eccentricity of the Hyperbola x2−2y2=6x ^ { 2 } - 2 y ^ { 2 } = 6x2−2y2=6

Find the Eccentricity of the Hyperbola $x ^ { 2 } - 2 y ^ { 2 } = 6$