The equation (x + 6)^2 + (y – 8)^2 = 81 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 equation of a circle centred at (x0,y0) and radius r is given by
(x-x0)²+(y-y0)²=r^2.
The posted equation therefore represents a circle with radius=√81, centred at (-6,8).
Continue with interpreting the results to complete the answer.
To describe the position of the source and the range of the signals in the given equation, we need to understand the standard form of the equation of a circle.
The standard equation of a circle with its center at the point (h, k) and a radius of r is given by:
(x - h)^2 + (y - k)^2 = r^2
Comparing this with the given equation, (x + 6)^2 + (y – 8)^2 = 81, we can determine the position and range of the radio signal source.
In the given equation, the center of the circle is (-6, 8), and the radius is the square root of 81, i.e., 9.
Therefore, the position of the source of the radio signal is at the point (-6, 8). It represents the coordinates of the center of the circle.
The range of the radio signals can be determined by the radius of the circle, which is given as 9 units. This means that any point within a distance of 9 units from the center (-6, 8) will be within the range of the radio signals.
In summary, the source of the radio signal is positioned at (-6, 8), and the range of the signals extends up to 9 units from the center.