x28xy210y250 Determine the xy coordinates of the center of t

x^2-8x+y^2-10y+25=0 Determine the (x,y) coordinates of the center of the circle defined by the following equation.

Solution

The general equation of the circle is x² + y² + 2gx + 2fy + c = 0, where g = -h and f = -k, where h and k are the co-ordinates of the center.

The equation given is x² + y² - 8x - 10y + 25 = 0

Therefore 2gx = -8x   or g = -4 = - h Therefore h = 4

Similarly 2fy = -10y or f = -5 = -k . Therefore k = 5

The co -ordinates of the center are (h,k) = (4,5)