Find the eccentricity of the hyperbola.
-$$8 x ^ { 2 } - 9 y ^ { 2 } = 72$$
A) $\frac { \sqrt { 13 } } { 3 }$
B) $\frac { \sqrt { 17 } } { 3 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 3 } { 2 }$

Question

Quizplus · Accepted Answer

The given equation of the hyperbola is $8x^2 - 9y^2 = 72$. To find the eccentricity, we first write the equation in standard form: $\frac{x^2}{9} - \frac{y^2}{8} = 1$. The standard form of a hyperbola is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, where $a^2 = 9$ and $b^2 = 8$. The eccentricity $e$ of a hyperbola is given by $e = \sqrt{1 + \frac{b^2}{a^2}}$. Substituting $a^2 = 9$ and $b^2 = 8$, we get $e = \sqrt{1 + \frac{8}{9}} = \sqrt{\frac{17}{9}} = \frac{\sqrt{17}}{3}$.

Find the Eccentricity of the Hyperbola 8x2−9y2=728 x ^ { 2 } - 9 y ^ { 2 } = 728x2−9y2=72

Find the Eccentricity of the Hyperbola $8 x ^ { 2 } - 9 y ^ { 2 } = 72$