One focus of a hyperbola is located at (−1, 7). one vertex of the hyperbola is located at (−1, 5). the center is (−1, −3). what is the equation of the hyperbola?

So, if we plot those points, we'll end up with the picture below.

now, notice, the hyperbola is a vertical one, thus it has a vertical traverse axis, and since we know the center is at -1, -3, from there upwards straight up to the vertex at -1, 5, is 8 units, therefore, the "a" component is 8.

we also know that the distance from the center up to the focus point at -1,7 is 10 units, as you can see in the picture, therefore the distance "c" is 10.

since the hyperbola is a vertical one, the fraction with the positive sign, is the one with the "y" variable, and the equation for it will be like the one you see there in the picture, thus

The answer would be $68.04