SOLUTION: Find the center and the radius of the circle described by the equation x2+y2+8x-2y+15=0 How can I find the answer to this problem?

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Question 244635: Find the center and the radius of the circle described by the equation
x2+y2+8x-2y+15=0
How can I find the answer to this problem?
Found 2 solutions by Edwin McCravy, checkley77:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

Find the center and the radius of the circle described by the equation 

x%5E2%2By%5E2%2B8x-2y%2B15=0

Get the term in x next to the term in x%5E2
Get the term in y next to the term in y%5E2
Add -15 to both sides to get the constant on the right:

x%5E2%2B8x%2By%5E2-2y=-15

Multiply the coefficient of x, which is 8 by 1%2F2,
getting 4. Then square 4, getting 16.  Then add 
16 to both sides, writing it next to the term in x on
the left.

x%5E2%2B8x%2B16%2By%5E2-2y=-15%2B16

Multiply the coefficient of y, which is -2 by 1%2F2,
getting -1. Then square -1, getting %22%22%2B1.  Then add 
%22%22%2B1 to both sides, writing it next to the term in y on
the left.

x%5E2%2B8x%2B16%2By%5E2-2y%2B1=-15%2B16%2B1

Factor the first three terms on the left as a perfect square:
Factor the last three terms on the left as a perfect square:
Combine the numbers on the right side:

%28x%2B4%29%5E2%2B%28y-1%29%5E2=2

Compare that to the standard equation of a circle, which is:

%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2

where the center is %22%28h%2Ck%29%22

So h=-4, k=1, r%5E2=2

Therefore the center is the point %22%28h%2Ck%29%22=%22%28-4%2C1%29%22

And since 

r%5E2=2, we take the square root of both sides, 
and get

r=sqrt%282%29

So the radius of the circle is sqrt%282%29.

Edwin

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x2+y2+8x-2y+15=0
X^2+8X(+16)+Y^2-2Y+1)=15+16+1
(X+4)^2+(Y-1)^2=SQRT32
X+4=0
X=-4
Y-1=0
Y=1 (-4,0) IS THE CENTER.
RADIUS=SQRT32=5.6569