Question

Determine the center of the circle given by the equation x^2-8x+y^2-10y+5=0

Answer 1

Complete the squares in x and y.

Answer 2

complete the square via
\[x^2-8x+y^2-10y=-5\]
\[(x-4)^2+(y-5)^2=-5+4^2+5^2=36\]
center is (4,5) radius is
\[r=\sqrt{36}=6\]