# Math Help - origin of a circle

1. ## origin of a circle

Center of which circle is closer to the origin?

x2 + y2 + 6x + 6y = 21
x2 + y2 + 8x + 8y = 31
x2 + y2 — 12x — 12y = 43
x2 + y2 — 2x — 2y = 54

2. One thing you could do that would be good practice is to complete the square on each and see.

Take the first one:

$x^{2}+6x+y^{2}+6y=21$

$x^{2}+6x+9+y^{2}+6y+9=39$

$(x+3)^{2}+(y+3)^{2}=39$

This one has center at (-3,-3), Check the others.

But, by inspection, they're all pefect squares. Look at the coefficients of x and y. Which is the smallest?.