To describe the position of the source and the range of the signals, we need to rewrite the given equation in standard form:
(x + 9)^2 + (y - 4)^2 = 81
Expanding the square terms, we get:
x^2 + 18x + 81 + y^2 - 8y + 16 = 81
Simplifying, we get:
x^2 + y^2 + 18x - 8y + 16 = 0
Completing the square for x and y, we add and subtract the squares of half the x and y coefficients, respectively:
x^2 + 18x + 81 + y^2 - 8y + 16 = 0 + 81 + 16
(x + 9)^2 + (y - 4)^2 = 97
Comparing this to the standard form of a circle, (x - h)^2 + (y - k)^2 = r^2, we see that the center of the circle is (-9, 4) and the radius of the circle is sqrt(97), which represents the range of the radio signal. Therefore, the source of the radio signal is located at (-9, 4) and its range is sqrt(97).
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 the range of the signals
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3 answers
Oh, please! The original equation was
(x + 9)^2 + (y - 4)^2 = 81
and you dis a lot of useless (and erroneous) manipulation, and ended up with
(x + 9)^2 + (y - 4)^2 = 97
??? It started out as a circle, yet you could not seem to recognize that fact! The circle has radius 9.
(x + 9)^2 + (y - 4)^2 = 81
and you dis a lot of useless (and erroneous) manipulation, and ended up with
(x + 9)^2 + (y - 4)^2 = 97
??? It started out as a circle, yet you could not seem to recognize that fact! The circle has radius 9.
You are correct, I apologize for that error in my previous response. The given equation is indeed the equation of a circle with center at (-9, 4) and radius 9.
To see this, we can rewrite the equation in standard form as:
(x + 9)^2 + (y - 4)^2 = 81
This is in the form:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius. Comparing this to our equation, we see that the center is (-9, 4) and the radius is 9.
Therefore, the source of the radio signal is located at point (-9, 4) and the range of the signals extends to a distance of 9 units in all directions from the center.
To see this, we can rewrite the equation in standard form as:
(x + 9)^2 + (y - 4)^2 = 81
This is in the form:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius. Comparing this to our equation, we see that the center is (-9, 4) and the radius is 9.
Therefore, the source of the radio signal is located at point (-9, 4) and the range of the signals extends to a distance of 9 units in all directions from the center.
1 answer