The equation for the hyperbola is y^2/a^2 - x^2/b^2 = 1. You have a = 5/24 (although you miswrote it as 5/12 in the last line of your post), so now you need to find the value of 'b'. Use the formula c^2 = a^2 + b^2, where for a hyperbola 'c' = the distance from the center to each focus, which for this problem is 1/2 mile. Can you finish it from here?