Circle Center and Radius from Equation

Group and complete the square: (x² − 6x + 9) + (y² + 4y + 4) = 12 + 9 + 4, so (x − 3)² + (y + 2)² = 25. The center is (3, −2) and the radius is √25 = 5. The signs flip: −6x gives x − 3, so the center's x-coordinate is +3. TI-36X Pro tip: check the center by storing it: type 3, press sto→, tap the x yzt abcd key until x shows, then press enter; then type (−)2 and store it to y the same way. Now evaluate x² + y² − 6x + 4y − 12. The result is −25, and −(result) is r², so r = 5.