Question 80070
You first need to get your equation into the standard form, which is:
{{{(x-h)^2+(y-k)^2 = r^2}}} 

The center is then (h, k) and the radius is r.
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You are given: {{{x^2+y^2-4x+6y+4=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^2+y^2-4x+6y+4=0}}}
{{{x^2-4x+y^2+6y=-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^2-4x+4+y^2+6y+9=-4+4+9}}}
Simplifying the right side:
{{{x^2-4x+4+y^2+6y+9=9}}}
Now you can rewrite the x and y terms as factors which gets you in the needed format:
{{{(x-2)^2+(y+3)^2=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