Thread: 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

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

Take the first one:







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?.