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Question 495972: I know that the following equation will result in a circle graph (the teacher's key says so). But I would like to know how to get there. I need to isolate y:
x^2 + y^2 - 4y = 21
(that is, x squared plus y squared minus 4y equals 21)
Thank you
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! general form of a circle:
(x - h)^2 + (y - k)^2 = r^2
.
your equation:
x^2 + y^2 - 4y = 21
subtracting x^2 from both sides:
y^2 - 4y = -x^2 + 21
"complete the square" by adding 2 to both sides:
y^2 - 4y + 2 = -x^2 + 21 + 2
(y-2)(y-2) = -x^2 + 23
(y-2)^2 = -x^2 + 23
add x^2 to both sides:
x^2 + (y-2)^2 = 23 (equation of the circle)
.
Or, you can think of it as:
(x-0)^2 + (y-2)^2 = 23
Now, we can see the center is at (0,2)
with a radius of square root of 23
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