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

Question

Quizplus · Accepted Answer

The equation of the hyperbola is given in the form $Ax^2 - By^2 = C$, where $A = 8$, $B = 9$, and $C = 72$. To find the eccentricity $e$, we first need to bring the equation to its standard form by dividing the entire equation by $C$, resulting in $\frac{x^2}{9} - \frac{y^2}{8} = 1$. Here, $a^2 = 9$ and $b^2 = 8$, so $a = 3$ and $b = \sqrt{8}$. The eccentricity of a hyperbola is given by $e = \sqrt{1 + \frac{b^2}{a^2}}$. Substituting $a^2 = 9$ and $b^2 = 8$ into the formula gives $e = \sqrt{1 + \frac{8}{9}} = \sqrt{\frac{17}{9}} = \frac{\sqrt{17}}{3}$.

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

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