Find the Eccentricity of the conic. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$
A)Eccentricity: $e = \frac { \sqrt { 48 } } { 64 }$
B)Eccentricity: $e = \frac { \sqrt { 48 } } { 4 }$
C)Eccentricity: $e = \frac { \sqrt { 64 } } { 4 }$
D)Eccentricity: $e = \frac { \sqrt { 48 } } { 8 }$
E)Eccentricity: $e = \frac { \sqrt { 48 } } { 48 }$

Question

Find the Eccentricity of the conic.​ $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$ ​
A)Eccentricity: $e = \frac { \sqrt { 48 } } { 64 }$
B)Eccentricity: $e = \frac { \sqrt { 48 } } { 4 }$
C)Eccentricity: $e = \frac { \sqrt { 64 } } { 4 }$
D)Eccentricity: $e = \frac { \sqrt { 48 } } { 8 }$
E)Eccentricity: $e = \frac { \sqrt { 48 } } { 48 }$

Quizplus · Accepted Answer

The given equation is of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with $a^2 = 64$ and $b^2 = 16$. The eccentricity $e$ is given by $e = \sqrt{1 - \frac{b^2}{a^2}} = \sqrt{1 - \frac{16}{64}} = \sqrt{\frac{48}{64}} = \frac{\sqrt{48}}{8}$.

Find the Eccentricity of the Conic x264+y216=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 164x2​+16y2​=1

Find the Eccentricity of the Conic $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$