Question 226049
{{{x^2+y^2+12x+10y+57=0}}}
Rewrite the equation:
{{{x^2+12x+___+y^2+10y+___=-57+___+___}}}
We have to complete the square, so the blanks are filled in the {{{((1/2)*b)^2}}}
For the x: {{{((1/2)*12)^2=36}}}
So, we fill in the blank like:
{{{x^2+12x+36+y^2+10y+___=-57+36+___}}}
For the y: {{{((1/2)*10)^2=25}}}
{{{x^2+12x+36+y^2+10y+25=-57+36+25}}}
The x term and the y term have to be factored, but that's easy now since they are completed squares. The x-term is simply {{{(1/2)*12=6}}}, and the y-term is {{{(1/2)*10=5}}}. Like this:
{{{(x+6)^2+(y+5)^2=4}}}
The center is the opposite of what's in the parentheses:
(-6,-5), with a radius of 2 (because {{{2^2=4}}}).
Good luck!