Question 282458
given the equation of a circle x^2+y^2-10x+4y+13=0 find its center and its radius. im not sure i think its center is 10,-4 please help if possible

We need to get the equation in the standard form:

(x-h)^2 + (y-k)^2 = r^2.

In this form the center is at (h,k) with radius = r.

x^2 + y^2 - 10x + 4y + 13 = 0

(x^2 - 10x) + (y^2 + 4y) = -13

We can "complete the squares" by adding the same things to both sides:

(x^2 - 10x + 25) + (y^2 + 4y + 4) = -13 + 25 + 4

(x-5)^2 + (y+2)^2 = 16

The center is at (5,-2) and the radius is 4.