Finding an equation of a shiftd hyperbola with vertices

Question

Finding an equation of a shiftd hyperbola with vertices (-1, -1) (5, -1) and focuses (-4, -1) (8,-1) also find the equation of asymptotes of this hyperbola and sketch its graph 

Answer 1

The midpoint between the two vertices is (2,-1), the orientation is horizontal so, the starting point for our formula is

(x-2)²/a² - (y+1)²/b² = 1

the distance between the two vertices is 6, so a = 3

(x-2)²/9 - (y+1)²/b² = 1

the distance between the foci is 12, so c=6

c² = a² + b²
36 = 9 + b²
27 = b²
3√3 = b

thus
(x-2)²/9 - (y+1)²/27 = 1

the asymptotes will be through the point (2,-1)
and have the slopes ± 3√3/3 = ±√3