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

Question

Quizplus · Accepted Answer

The equation of the hyperbola is given in the form $x^2/a^2 - y^2/b^2 = 1$, where $a^2 = 25$ and $b^2 = 25$. The eccentricity $e$ of a hyperbola is given by $e = \sqrt{1 + b^2/a^2}$. Substituting $a^2 = 25$ and $b^2 = 25$, we get $e = \sqrt{1 + 25/25} = \sqrt{2} = \sqrt{26}/5$.

Find the Eccentricity e e e Of the Hyperbola x2−25y2=25x ^ { 2 } - 25 y ^ { 2 } = 25x2−25y2=25

Find the Eccentricity $e$ Of the Hyperbola $x ^ { 2 } - 25 y ^ { 2 } = 25$