The earthquake was felt up to 52 miles from its epicenter. you are located 40 miles west and 30 miles south of the epicenter. let the epicenter be (0,0) . find the standard equation that describes the boundary of the earthquake

For this problem, it is best to draw a plane showing the positive and negative, in x and y axes. 
Since it is given that the coordinates of the epicenter is at (0,0), thus it is at the center of the plane. 
In order to find the outside boundary of the earthquake, the center-radius equation can be used as follows:
[(x-h)^2] - [(y-k)^2] = r^2

where, (h,k) is the coordinates of the center, which is (0,0), and r is the radius which is equal to 52.

Substituting these values into the standard center-radius equation,
x^2 - y^2 = 52^2

The answer is,

x^2 - y^2 = 2704