Find the eccentricity of the ellipse.
-$$64 x ^ { 2 } + 4 y ^ { 2 } = 256$$
A) $\sqrt { 15 }$
B) $\frac { \sqrt { 15 } } { 8 }$
C) $\frac { \sqrt { 15 } } { 4 }$
D) $\frac { \sqrt { 17 } } { 4 }$

Question

Quizplus · Accepted Answer

The given equation of the ellipse is $64x^2 + 4y^2 = 256$. To find the eccentricity, we first write the equation in standard form by dividing each term by 256: $\frac{x^2}{4} + \frac{y^2}{64} = 1$. Here, $a^2 = 64$ and $b^2 = 4$, 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 $e = \sqrt{1 - \frac{4}{64}} = \sqrt{1 - \frac{1}{16}} = \sqrt{\frac{15}{16}} = \frac{\sqrt{15}}{4}$.

Find the Eccentricity of the Ellipse 64x2+4y2=25664 x ^ { 2 } + 4 y ^ { 2 } = 25664x2+4y2=256

Find the Eccentricity of the Ellipse $64 x ^ { 2 } + 4 y ^ { 2 } = 256$