SOLUTION: Given that the equation of a circle is x^2+y^2-10x+4y+13=0, find its center and its radius.

Question 183194: Given that the equation of a circle is x^2+y^2-10x+4y+13=0, find its center and its radius.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Subtract 13 from both sides.

Group like terms.

Take half of the "x" coefficient -10 to get -5. Square it to get 25. Add this to both sides.

Take half of the "y" coefficient 4 to get 2. Square that result to get 4. Add this to both sides.

Combine like terms.

Factor to get

Factor to get

Rewrite as

Rewrite as

So the equation is now in the form (which is a circle) where (h,k) is the center and "r" is the radius

We can see that , , and

So the center is (5,-2) and the radius is 4 units
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