(-3,-2) (7,-2) this will be a parabola that opens sideways
2a =the distance between the vertices
2a = (7 - -3) = 10
a = 5 ..... a^2 = 25
2c = the distance between the foci
2c = (12 - -8)
2c = 20
c =10 ..... c^2 =100
c^2 - a^2 = b^2
b^2 = 10^2 - 5^2 = 75
The center is [ (-3 + 7)/2 , -2 ] = [ 4/2, -2]= (2, -2) =(h , k)
The equation is
( x -h)^2 (y - k)^2
_______ - ________ = 1
a^2 b^2
( x - 2)^2 ( x + 2)^2
_______ - _________ = 1
25 75
Here's a graph : https://www.desmos.com/calculator/jkmg428rig