Question 372682
Complete the square in {{{x}}} and {{{y}}}.
{{{2x^2+2y^2+24x+28y+138=0}}}
{{{x^2+12x+y^2+14y+69=0}}}
{{{(x^2+12x+36)+(y^2+14y+49)+69=36+49}}}
{{{(x+6)^2+(y+7)^2=85-69}}}
{{{highlight((x+6)^2+(y+7)^2=16)}}}
Compare to the general equation for a circle centered at ({{{h}}},{{{k}}}) with a radius {{{R}}}:
{{{(x-h)^2+(y-k)^2=R^2}}}