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.
position is the center of the circle: (-6,-4)
Range is the radius of the circle: 6
The equation (x + 6)2 + (y + 4)2 = 36 represents a circle in the coordinate plane. Let's break it down to understand its components.
The equation is in the form (x - h)2 + (y - k)2 = r2, where (h, k) represents the center of the circle, and r represents the radius.
Comparing this equation to the given equation (x + 6)2 + (y + 4)2 = 36, we can see that the center of the circle is at the point (-6, -4) and the radius is √36, which is 6.
Therefore, the position of the source of the radio signal is at the coordinates (-6, -4). This point represents the center of the circle, where the radio signal originates.
The range of the signal is the distance from the center of the circle to any point on the circumference of the circle. In this case, the radius is 6, so the range of the signal extends 6 units in all directions from the center.
To visualize this, imagine a circle with its center at (-6, -4) and a radius of 6 units. The entire range of the signal would then be any point on the boundary of this circle. Anything outside this circle would be out of the range of the radio signal.
Thus, the position of the source of the radio signal is at (-6, -4), and the range of the signal extends 6 units in all directions from the center.