Find the eccentricity of the ellipse.
-$$x ^ { 2 } + 4 y ^ { 2 } = 4$$
A) $\frac { \sqrt { 3 } } { 2 }$
B) $\sqrt { 3 }$
C) $\frac { \sqrt { 5 } } { 2 }$
D) $\sqrt { 5 }$

Question

Quizplus · Accepted Answer

The given equation of the ellipse is $x^2 + 4y^2 = 4$. Dividing the entire equation by 4 to get it in standard form, we get $\frac{x^2}{2^2} + \frac{y^2}{1^2} = 1$. Here, $a^2 = 4$ and $b^2 = 1$, where $a$ is the semi-major axis and $b$ is the semi-minor axis. The eccentricity $e$ of an ellipse is given by $e = \sqrt{1 - \frac{b^2}{a^2}}$. Substituting the values, we get $e = \sqrt{1 - \frac{1}{4}} = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}$.

Find the Eccentricity of the Ellipse x2+4y2=4x ^ { 2 } + 4 y ^ { 2 } = 4x2+4y2=4

Find the Eccentricity of the Ellipse $x ^ { 2 } + 4 y ^ { 2 } = 4$