Find the eccentricity $ e $ of the ellipse.
-$$x ^ { 2 } + 25 y ^ { 2 } = 25$$
A) $2 \sqrt { 6 }$
B) $\frac { 2 \sqrt { 6 } } { 5 }$
C) $\frac { \sqrt { 26 } } { 5 }$
D) $\sqrt { 26 }$

Question

Quizplus · Accepted Answer

The equation of the ellipse is in the standard form $\frac { x ^ { 2 } } { b ^ { 2 } } + \frac { y ^ { 2 } } { a ^ { 2 } } = 1$, where $a$ and $b$ are the semi-major and semi-minor axes, respectively. In this case, $a = 5$ and $b = 1$. The eccentricity is given by $e = \sqrt { 1 - \frac { b ^ { 2 } } { a ^ { 2 } } } = \sqrt { 1 - \frac { 1 } { 25 } } = \frac { 2 \sqrt { 6 } } { 5 }$.

Find the Eccentricity e e e Of the Ellipse x2+25y2=25x ^ { 2 } + 25 y ^ { 2 } = 25x2+25y2=25

Find the Eccentricity $e$ Of the Ellipse $x ^ { 2 } + 25 y ^ { 2 } = 25$