Question

The equation (x-4)^2 + (y-2)^2 =169 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals.

Answer 1

This is the equation for a circle. The center of the circle is the source and the outside of the circle is the radio signal. x-4 notes the x-coordinate (or "h") of the center of the circle, and y-2 notes the y-coordinate (or "k") of the center of the circle. Therefore, the center of the circle sits at (4,2). The formula for a circle is (x-h)^2 + (y-k)^2 = r^2. So the 169 is the square of the radius, which is 13. So the source sits at (4, 2) and the signals are at a radius length of 13, or 13 units from the center.