The equation (x + 6)2 + (y + 4)2 = 36 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals???
The center of the circle is at (-6, -4), which is the position of the source of the radio signal. The radius of the circle is 6, which means the range of the signals is up to 6 units in any direction from the source.
To describe the position of the source and the range of the signals modeled by the equation (x + 6)² + (y + 4)² = 36, we can analyze the equation in standard form:
(x + 6)² + (y + 4)² = 36
This equation represents a circle centered at the point (-6, -4) with a radius of 6. The general equation of a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius.
Therefore, the position of the source of the radio signal is at the point (-6, -4), which corresponds to the center of the circle. The signal range extends up to a distance of 6 units from the center in all directions. This means that any point on the circumference of the circle represents the maximum range at which the radio signal can be received.