SOLUTION: Find the center and radius of the following circle: x2 + y2 - 12x + 8y - 29 = 0

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Question 1121380: Find the center and radius of the following circle:
x2 + y2 - 12x + 8y - 29 = 0
Found 3 solutions by josgarithmetic, MathLover1, Alan3354:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-12x%2By%5E2%2B8y=29
x%5E2-12x%2B36%2By%5E2%2B8y%2B16=29%2B36%2B16
%28x-6%29%5E2%2B%28y%2B4%29%5E2=81
%28x-6%29%5E2%2B%28y%2B4%29%5E2=9%5E2

CENTER (6,-4)
RADIUS 9

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
to find the center and radius of the following circle, write given equation in this form:
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 where h and k are x and y coordinates of the center, and r is the radius

x%5E2+%2B+y%5E2+-+12x+%2B+8y+-+29+=+0+ ......rearrange and group
%28x%5E2++-+12x%29+%2B+%28y%5E2%2B+8y+%29+=+29+.... complete squares
%28x%5E2++-+12x%2Bb%5E2%29-b%5E2+%2B+%28y%5E2%2B+8y%2Bb%5E2+%29+-b%5E2=+29+
recall the rule: %28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2
since you have 2ab=12 and a=1, =>b=6 for x part
and 2ab=8 and a=1, =>b=4 for y part
than you have:
%28x++-+6%29%5E2-6%5E2+%2B+%28y%2B+4%29%5E2++-4%5E2=+29+
%28x++-+6%29%5E2-36+%2B+%28y%2B+4%29%5E2++-16=+29+
%28x++-+6%29%5E2%2B+%28y%2B+4%29%5E2++-52=+29+
%28x++-+6%29%5E2%2B+%28y%2B+4%29%5E2++=+29%2B52+
%28x++-+6%29%5E2%2B+%28y%2B+4%29%5E2++=+81+
%28x++-+6%29%5E2%2B+%28y%2B+4%29%5E2++=+9%5E2+
now you see that:
h=6 and k=-4 and the center is at (6, -4)
and the radius is 9

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the center and radius of the following circle:
x2 + y2 - 12x + 8y - 29 = 0
-----
Complete the square for x and for y.
x^2 - 12x + y^2 + 8y - 29 = 0
x^2 - 12x + y^2 + 8y = 29
x^2 - 12x + 36 + y^2 + 8y + 16 = 29+36+16 = 81
(x-6)^2 + (y+4)^2 = 9^2
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(x-h)^2 + (y-k)^2 = r^2 is a circle - center at (h,k), radius r