Final answer:
To find a hyperbola with one focus point in common with the given hyperbola, we need to shift the center of the hyperbola horizontally by the same amount. The equation of the new hyperbola is (y+11)^2/(15^2)-(x-15)^2/(8^2)=1.
Step-by-step explanation:
The hyperbola that has one focus point in common with the hyperbola (y+11)^2/(15^2)-(x-7)^2/(8^2)=1 is obtained by shifting the given hyperbola horizontally. The general form of a hyperbola is given by (y-k)^2/a^2 - (x-h)^2/b^2 = 1, where (h,k) represents the center of the hyperbola. In this case, the center of the given hyperbola is (7,-11). To find a hyperbola with the same focus point, we can shift the center horizontally by the same amount.
Let's denote the center of the new hyperbola as (h,k). Since we want one focus point in common, the x-coordinate of the new center will be h = 7 + 8 = 15. The y-coordinate remains the same, so k = -11. The equation of the new hyperbola is then (y+11)^2/(15^2)-(x-15)^2/(8^2)=1.