Find the eccentricity of the ellipse.
-$$23 x ^ { 2 } + y ^ { 2 } = 23$$
A) $\frac { 4 \sqrt { 33 } } { 23 }$
B) $\frac { \sqrt { 23 } } { 22 }$
C) $\frac { 23 } { 4 \sqrt { 33 } }$
D) $\frac { \sqrt { 506 } } { 23 }$

Question

Quizplus · Accepted Answer

The given equation is $\frac{x^2}{1} + \frac{y^2}{23} = 1$, indicating a vertical ellipse. The eccentricity $e$ is given by $e = \sqrt{1 - \frac{a^2}{b^2}}$, where $a^2 = 1$ and $b^2 = 23$. Thus, $e = \sqrt{1 - \frac{1}{23}} = \sqrt{\frac{22}{23}} = \frac{\sqrt{506}}{23}$.

Find the Eccentricity of the Ellipse 23x2+y2=2323 x ^ { 2 } + y ^ { 2 } = 2323x2+y2=23

Find the Eccentricity of the Ellipse $23 x ^ { 2 } + y ^ { 2 } = 23$