Standard form of the equation of a hyperbola that has vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).

Check the picture below.  So with those points, ther hyperbola looks more or less like so.

now, notice the distance from vertex to vertex, half-way is the center, at 30, -15.

now, from the center to the given focus point, at -11, - 15, is 41 units, bear in mind the distance from the center to either foci is "c".  Thus c = 41

since the traverse axis for the hyperbola is the x-axis, thus the fraction with the "x" variable is the positive fraction.  thus