Answer:
b^2 = 5, a^2 = 4 and k= -2.
Explanation:
In this case we have the first focus (-2, -2), the center (1, -2) and from the graph we can deduce that the distance between the vertices 2a is 4. So 2a=5 then a=2, thus, a^2 = 4.
The hyperbola is centered at the point (h, k) = (1, -2) thus we can conclude that h=1 and k = -2.
We can deduce from the graph that the distance from the center to each focus is 3, so c=3. (c represents de distance from center to focus).
We know that c^2 = a^2 + b^2
Solving for b^2, we have that:
b^2 = c^2 - a^2 = 3^2 - 2^2 = 5
Then b^2 = 5