(x − h)² + (y − k)² = r² hides two things a student has to un-hide: the centre’s signs are reversed, and the right-hand side is r² rather than r. These free printable worksheets ask for both, from either form.
If they get stuck
The answer key prints on a separate page.
Standard form looks like it can be read straight off, and it can — but the two reversals catch nearly everybody. (x − 3)² means the centre is at +3, not −3, and = 25 means the radius is 5, not 25. A page of these is worth having on its own, before any completing the square, precisely because the errors are in the reading rather than the working.
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.
Find the center and radius of x² + y² + 4y − 32 = 0
