A lowwattage radio station can be heard only within a certai

A low-wattage radio station can be heard only within a certain distance from the station. On the graph below, the circular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. Which equation represents the boundary for the region where the station can be heard?

Solution

From the graph, the center of the circle can be found as x co-ordinate = -6 and y co ordinate = -1(approximately), i.e the center = (-6,-1) and the radius is 4 units

The equation of the circle is given by the equation (x-h)² + (y-k)² = r², where h and k are the co-ordinates of the center.

Therefore [x-(-6)]² + [y-(-1)]² = 4²

Therefore (x+6)² + (y+1)² = 16. Solving, we get

x² + 12x + 36 + y² + 2y + 1 - 16 = 0

x² + y² + 12x + 2y + 21 = 0 is the required equation of the circle.