Answer:
(x+1)^2/9 - (y-2)^2/16 = 1
Step-by-step explanation:
As the center and the vertex of the hyperbola forms a horizontal segment (they have the same y value), we can use the hyperbola equation with horizontal axis:
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
For this equation, the center of the hyperbola is (h,k), the vertix is (h±a, k) and the focus is (h±c, k), where c^2 = a^2 + b^2
So if the center is (-1,2), we have h = -1 and k = 2
If the vertex is (-4,2), we have that h-a = -4, so a = 3
If the focus is (-6,2), we have that h-c = -6, so c = 5
Now, finding b, we have:
5^2 = 3^2 + b^2
b = 4
So our equation is:
(x+1)^2/9 - (y-2)^2/16 = 1
