+129852 a = the distance between the center and the vertex (-4,3) and ( -4,7) = 4
The slope of one of the asymptotes is given by
a/b = 2
4 / b = 2 / 1 and we can write
b / 4 = 1 / 2 multiply both sides by 4
b = 2
The equation of the hyperbola is
(y - 3)^2 (x +4)^2
_______ - _________ = 1
a^2 b^2
(y - 3)^2 (x + 4)^2
_______ - _________ = 1
16 4
See the graph here : https://www.desmos.com/calculator/dpspqazdsc
