SOLUTION: Find the center and the radius of the circle give by x^2+8x+y^2+6y-24=0

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Question 105703: Find the center and the radius of the circle give by
x^2+8x+y^2+6y-24=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of a circle centered at (h,k) with radius, R, is given by:
%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2
%28x%5E2-2hx%2Bh%5E2%29%2B%28y%5E2-2ky%2Bk%5E2%29=R%5E2
%28x%5E2-2hx%29%2B%28y%5E2-2ky%29=R%5E2-h%5E2-k%5E2
Let's look at your equation and compare terms.
%28x%5E2%2B8x%29%2B%28y%5E2%2B6y%29-24=0
%28x%5E2%2B8x%29%2B%28y%5E2%2B6y%29=24
Comparing,
1.-2hx=8x
2.-2ky=6y
3.R%5E2-h%5E2-k%5E2=24
From 1,
1.-2hx=8x
h=-4
From 2,
2.-2ky=6y
k=-3
From 3,
3.R%5E2-h%5E2-k%5E2=24
R%5E2-%28-4%29%5E2-%28-3%29%5E2=24
R%5E2-16-9=24
R%5E2=49
R=7
Putting those values back in the first equation,
%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2
%28x-%28-4%29%29%5E2%2B%28y-%28-3%29%29%5E2=49
highlight%28%28x%2B4%29%5E2%2B%28y%2B3%29%5E2=49%29
A circle centered at (-4,-3) with a radius of 7.
Let's verify.
%28x%2B4%29%5E2%2B%28y%2B3%29%5E2=49
%28x%5E2%2B8x%2B16%29%2B%28y%5E2%2B6y%2B9%29=49
x%5E2%2B8x%2By%5E2%2B6y%2B25-49=49-49
x%5E2%2B8x%2By%5E2%2B6y-24=0
Back to your original equation. Good answer.