Write the standard form of the equation of the hyperbola subject to the given conditions.
-Vertices: $( - 10 , - 5 ) , ( 2 , - 5 )$
Slope of the asymptotes: $\pm \frac { 1 } { 2 }$
A) $\frac { ( x + 4 ) ^ { 2 } } { 9 } - \frac { ( y + 5 ) ^ { 2 } } { 36 } = 1$
B) $\frac { ( y + 5 ) ^ { 2 } } { 9 } - \frac { ( x + 4 ) ^ { 2 } } { 36 } = 1$
C) $\frac { ( x + 4 ) ^ { 2 } } { 36 } - \frac { ( y + 5 ) ^ { 2 } } { 9 } = 1$
D) $\frac { ( y + 5 ) ^ { 2 } } { 36 } - \frac { ( x + 4 ) ^ { 2 } } { 9 } = 1$

Question

Quizplus · Accepted Answer

The center of the hyperbola is the midpoint of the vertices, $(-4, -5)$. The distance between the vertices is 12, so $2a = 12$ and $a = 6$. The slope of the asymptotes is $\pm \frac{b}{a} = \pm \frac{1}{2}$, so $b = 3$. The equation is $\frac{(x + 4)^2}{36} - \frac{(y + 5)^2}{9} = 1$.

Write the Standard Form of the Equation of the Hyperbola (−10,−5),(2,−5)( - 10 , - 5 ) , ( 2 , - 5 )(−10,−5),(2,−5)

Write the Standard Form of the Equation of the Hyperbola $( - 10 , - 5 ) , ( 2 , - 5 )$