Question

The University of Southern California is located about 2.5 miles west and about 2.8 miles south of downtown Los Angeles. Suppose an earthquake occurs with its epicenter about 40 miles from the university. Assume that the origin of a coordinate plane is located at the center of downtown Los Angeles. Write an equation for the set of points that could be the epicenter of the earthquake.

Answer 1

If x represents distance measured east of downtown, and y represents distance measured north of downtown, the circle of radius 40 centered at (-2.5, -2.8) will have an equation of the form
(x - h)² + (y - k)² = r²
where the center is (h, k) and the radius is r. The locus of points 4 miles from USC will satisfy the equation
(x +2.5)² + (y + 2.8)² = 1600