Question

What is the radius of a circle whose equation is x2+y2+8x−6y+21=0?

Answer 1

Complete the square:

x^2 + 8x = (x + 4)^2 − 16
y^2 − 6y = (y − 3)^2 − 9

So
(x + 4)^2 − 16 + (y − 3)^2 − 9 + 21 = 0
⇒ (x + 4)^2 + (y − 3)^2 = 4

Thus the radius is √4 = 2.