The equation (x + 9)^2 + (y - 4)^2 = 81 models the position and range of the source of a radio signal. Describe the position of the source and range of the signals.
The center of the circle is (-9,4) and the radius is 9. Therefore, the source of the radio signal is located at (-9,4) and the range of the signal extends up to a distance of 9 units in all directions from the source.
To describe the position and range of the source of the radio signal, we can analyze the given equation:
(x + 9)^2 + (y - 4)^2 = 81
This equation represents a circle in the Cartesian coordinate system. The general equation for a circle is (x - a)^2 + (y - b)^2 = r^2, where (a, b) represents the center of the circle and r represents the radius.
Comparing the equation with the general form, we can determine the properties of the source of the radio signal:
1. Center: The center of the circle is given by the opposite sign of the constants in the equation. In this case, the center of the circle is at (-9, 4).
2. Range: The range of the signal, or the radius of the circle, is determined by taking the square root of the constant on the right side of the equation. In this case, the radius is √81 = 9.
Therefore, the position of the source of the radio signal is at (-9, 4), and the range of the signal extends to a radius of 9 units.