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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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## Answers ( )

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 = 81One 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.