Find the centre or the radius of a circle from its equation

Follow this one with me, a step at a time. Try to guess each step first.

Worked example 1

Find the centre of the circle x² + y² − 14x + 2y − 7 = 0.

Remember: For x² + y² + Dx + Ey + F = 0 the centre is (−D/2, −E/2). The radius comes from r² = (D/2)² + (E/2)² − F.

Here D = −14 and E = 2.
Half of each, with its sign changed, gives the centre (7, −1).

Common mistakes

Changed the sign of one coefficient and not the other. Both change.
Kept the signs of the coefficients. The centre is (−D/2, −E/2).
Gave the square of the radius. Take the square root.