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

Question

Quizplus · Accepted Answer

The standard form of an ellipse equation is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $a$ and $b$ are the semi-major and semi-minor axes, respectively. For the given equation $x^2 + 2y^2 = 6$, it can be rewritten as $\frac{x^2}{6} + \frac{y^2}{3} = 1$, indicating $a^2 = 6$ and $b^2 = 3$. The eccentricity $e$ of an ellipse is given by $e = \sqrt{1 - \frac{b^2}{a^2}}$. Substituting $a^2 = 6$ and $b^2 = 3$ gives $e = \sqrt{1 - \frac{3}{6}} = \sqrt{\frac{1}{2}} = \frac{\sqrt{2}}{2}$.

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

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