x² + y² − 6x + 4y − 12 = 0 is a circle, but it gives up neither its center nor its radius until two squares are completed. These free printable worksheets start from general form, and the answer key writes every line down to (x − h)² + (y − k)² = r² and the center and radius read off it.
If they get stuck
The answer key prints on a separate page.
The last line of every answer is standard form, and reading it is where the marks are lost even after the algebra is right: (x − 3)² puts the center at +3, not −3, and = 25 means the radius is 5, not 25. A page that only asks for that reading — no completing the square — is worth doing first, and it has a sheet of its own.
General form is what the standard asks for: x² + y² − 6x + 4y − 12 = 0 gives up nothing until two squares are completed. The method is the one from quadratics with a second variable along for the ride — group the x terms, group the y terms, halve-and-square each linear coefficient, add both to each side. The answer key writes every line.
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
The equation of a circle, step by step