Find an equation for the hyperbola described.
-Vertices $\left( \frac { 1 } { 2 } , - 3 \right)$ and $\left( - \frac { 9 } { 2 } , - 3 \right) ;$ asymptotes $y + 3 = \pm \frac { 6 } { 5 } ( x + 2 )$
A) $\frac { ( x + 2 ) ^ { 2 } } { 9 } - \frac { 4 ( y + 3 ) ^ { 2 } } { 25 } = 1$
B) $\frac { 4 ( x + 2 ) ^ { 2 } } { 25 } - \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$
C) $\frac { ( y + 3 ) ^ { 2 } } { 9 } - \frac { 4 ( x + 2 ) ^ { 2 } } { 25 } = 1$
D) $\frac { 4 ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$

Question

Quizplus · Accepted Answer

The hyperbola is horizontal with center at $(-4, -3)$, vertices along the x-axis, and asymptotes with slope $\pm \frac{6}{5}$. The equation is $\frac{(x+2)^2}{25/4} - \frac{(y+3)^2}{9} = 1$, which simplifies to choice B.

Find an Equation for the Hyperbola Described (12,−3)\left( \frac { 1 } { 2 } , - 3 \right)(21​,−3)

Find an Equation for the Hyperbola Described $\left( \frac { 1 } { 2 } , - 3 \right)$