Write an equation for the hyperbola.
-vertices at $( - 7,4 ) , ( - 7 , - 16 )$; asymptotes $y = \pm \frac { 10 } { 2 } ( x + 7 ) - 6$
A) $\frac { ( y + 6 ) ^ { 2 } } { 100 } - \frac { ( x + 7 ) ^ { 2 } } { 4 } = 1$

B) $\frac { ( y - 6 ) ^ { 2 } } { 100 } - \frac { ( x - 7 ) ^ { 2 } } { 4 } = 1$

C) $\frac { ( x + 7 ) ^ { 2 } } { 100 } - \frac { ( y + 6 ) ^ { 2 } } { 100 } = 1$

D) $\frac { ( x - 7 ) ^ { 2 } } { 100 } - \frac { ( y - 6 ) ^ { 2 } } { 100 } = 1$

Question

Write an equation for the hyperbola.
-vertices at $( - 7,4 ) , ( - 7 , - 16 )$; asymptotes $y = \pm \frac { 10 } { 2 } ( x + 7 ) - 6$
A) $\frac { ( y + 6 ) ^ { 2 } } { 100 } - \frac { ( x + 7 ) ^ { 2 } } { 4 } = 1$

B) $\frac { ( y - 6 ) ^ { 2 } } { 100 } - \frac { ( x - 7 ) ^ { 2 } } { 4 } = 1$

C) $\frac { ( x + 7 ) ^ { 2 } } { 100 } - \frac { ( y + 6 ) ^ { 2 } } { 100 } = 1$

D) $\frac { ( x - 7 ) ^ { 2 } } { 100 } - \frac { ( y - 6 ) ^ { 2 } } { 100 } = 1$

Quizplus · Accepted Answer

The vertices indicate the hyperbola is vertical, and the center is at $(-7, -6)$. The distance between vertices is $20$, so $a=10$, and the slope of the asymptotes gives $b=5$. Thus, the equation is $\frac{(y+6)^2}{100} - \frac{(x+7)^2}{25} = 1$, which simplifies to choice A.

Write an Equation for the Hyperbola (−7,4),(−7,−16)( - 7,4 ) , ( - 7 , - 16 )(−7,4),(−7,−16)

Write an Equation for the Hyperbola $( - 7,4 ) , ( - 7 , - 16 )$