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Write the equation of the circle whose center is (-4,8) and has a diameter of 18
Question
Write the equation of the circle whose center is (-4,8) and has a diameter of 18
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Mathematics
3 years
2021-09-04T08:57:39+00:00
2021-09-04T08:57:39+00:00 1 Answers
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Answer:
(x + 4)^2 + (y – 8)^2 = 81
or
(x + 4)^2 + (y – 8)^2 = 9^2 depending on how your teacher wants it written.
Step-by-step explanation:
The standard form for a circle is
(x + h)^2 + (y + k)^2 = r^2
r is the radius.
You are given the diameter
r = d/2
r = 18/2
r = 9
So you already have the right hand side of the equation
(x + h)^2 + (y + k)^2 = 9*2
(x + h)^2 + (y + k)^2 = 81
You basically have h and k as well. They come from the center point.
h = 4
k = – 8
So the equation of the circle (and the answer) is
(x + 4)^2 + (y – 8)^2 = 81
One question remains. Why do the x and y values change signs? If you know what the distance formula is, then what you are finding is the distance r of all points on the circle from the center of the circle.
It is the distance formula that is actually the formula for the circle.