Find the eccentricity of the ellipse. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 1$
A)Eccentricity: $e = \frac { 8 \sqrt { 17 } } { 17 }$
B)Eccentricity: $e = \frac { \sqrt { 17 } } { 9 }$
C)Eccentricity: $e = - \frac { \sqrt { 17 } } { 9 }$
D)Eccentricity: $e = \frac { \sqrt { 17 } } { 17 }$
E)Eccentricity: $e = - \frac { 9 \sqrt { 17 } } { 9 }$

Question

Find the eccentricity of the ellipse.  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 1$ 
A)Eccentricity: $e = \frac { 8 \sqrt { 17 } } { 17 }$
B)Eccentricity: $e = \frac { \sqrt { 17 } } { 9 }$
C)Eccentricity: $e = - \frac { \sqrt { 17 } } { 9 }$
D)Eccentricity: $e = \frac { \sqrt { 17 } } { 17 }$
E)Eccentricity: $e = - \frac { 9 \sqrt { 17 } } { 9 }$

Quizplus · Accepted Answer

The eccentricity $e$ of an ellipse given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is $e = \sqrt{1 - \frac{b^2}{a^2}}$, where $a$ is the semi-major axis and $b$ is the semi-minor axis. For the given ellipse $\frac{x^2}{64} + \frac{y^2}{81} = 1$, $a^2 = 81$ and $b^2 = 64$, so $e = \sqrt{1 - \frac{64}{81}} = \sqrt{\frac{17}{81}} = \frac{\sqrt{17}}{9}$.

Find the Eccentricity of the Ellipse x264+y281=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 164x2​+81y2​=1

Find the Eccentricity of the Ellipse $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 1$