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

Question

Quizplus · Accepted Answer

The given equation can be rewritten in standard form as $\frac{x^2}{6} + \frac{y^2}{3} = 1$. Here, $a^2 = 6$ and $b^2 = 3$. The eccentricity $e$ is given by $e = \sqrt{1 - \frac{b^2}{a^2}} = \sqrt{1 - \frac{3}{6}} = \sqrt{\frac{1}{2}} = \frac{\sqrt{2}}{2}$.

Find the Eccentricity of the Ellipse x2+2y2=6x ^ { 2 } + 2 y ^ { 2 } = 6x2+2y2=6

Find the Eccentricity of the Ellipse $x ^ { 2 } + 2 y ^ { 2 } = 6$