Each of three stations in a seismograph network has detected an earthquake in their region. Seismograph readings indicate that the epicenter of the earthquake is 50 kilometers from the first station, 40 kilometers from the second station, and 13 kilometers from the third station. On a map in which each grid represents one square kilometer, the first station is located at the origin, the second station at (0, 30), and the third station at (35, 18).
a. Write a system of second-degree equations that models this situation.
b. Graph the system and use the graph to approximate the location of the epicenter.
c. Solve the system of equations algebraically to determine the location of the epicenter