Write an equation for the hyperbola.
-vertices at $( - 5,3 ) , ( - 5 , - 19 ) ;$ asymptotes $y = \pm \frac { 11 } { 4 } ( x + 5 ) - 8$
A) $\frac { ( y - 8 ) ^ { 2 } } { 121 } - \frac { ( x - 5 ) ^ { 2 } } { 16 } = 1$
B) $\frac { ( x - 5 ) ^ { 2 } } { 121 } - \frac { ( y - 8 ) ^ { 2 } } { 121 } = 1$
C) $\frac { ( y + 8 ) ^ { 2 } } { 121 } - \frac { ( x + 5 ) ^ { 2 } } { 16 } = 1$
D) $\frac { ( x + 5 ) ^ { 2 } } { 121 } - \frac { ( y + 8 ) ^ { 2 } } { 121 } = 1$

Question

Quizplus · Accepted Answer

The center of the hyperbola is the midpoint of the vertices, which is $(-5, -8)$. The distance between the vertices (22 units) is $2a$, so $a=11$ and $a^2=121$. The slope of the asymptotes $\pm\frac{11}{4}$ gives the ratio $\frac{a}{b}$, so $b=4$ and $b^2=16$. Since the vertices are vertical, the $y$-term is positive, leading to the equation $\frac{(y+8)^2}{121} - \frac{(x+5)^2}{16} = 1$.

Write an Equation for the Hyperbola (−5,3),(−5,−19);( - 5,3 ) , ( - 5 , - 19 ) ;(−5,3),(−5,−19);

Write an Equation for the Hyperbola $( - 5,3 ) , ( - 5 , - 19 ) ;$