Question

given the equation
x^2-2x+y^2+10y-170=0,
complete the square for both x and y and find the equation of the circle.

Answer 1

\[x^2-2x+y^2+10y-170=0\]complete squares; move constant to RHS\[(x^2-2x+1)+(y^2+10y+25=170+1+25\]factor each group as perfect square trinomial\[(x-1)^2+(y+5)^2=196\]The center is (1,-5), the radius is 14