SOLUTION: x^2+y^2-4x+6y+4=0 i need to find the center, and radius

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Question 80070: x^2+y^2-4x+6y+4=0

i need to find the center, and radius

Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
You first need to get your equation into the standard form, which is:
%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2
The center is then (h, k) and the radius is r.
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You are given: x%5E2%2By%5E2-4x%2B6y%2B4=0, so the first step is to put this into the above form. The technique you need to use is called "Completing The Square." First, I will rewrite the equations a bit to organize the terms properly as follows:
x%5E2%2By%5E2-4x%2B6y%2B4=0
x%5E2-4x%2By%5E2%2B6y=-4
Now comes the Completing The Square part...divide the coefficients of x and y respectively by 2 and square the result. Add this number to both sides of the equation in order to maintain the equality:
x%5E2-4x%2B4%2By%5E2%2B6y%2B9=-4%2B4%2B9
Simplifying the right side:
x%5E2-4x%2B4%2By%5E2%2B6y%2B9=9
Now you can rewrite the x and y terms as factors which gets you in the needed format:
%28x-2%29%5E2%2B%28y%2B3%29%5E2=9
Now that you have the equation in the proper format, you can easily get the center and the radius.
Good Luck,
tutor_paul@yahoo.com