Find the centre and radius of the circles x² + y² – 4x – 8y – 45 = 0.

The given equation is

x² + y² – 4x – 8y – 45 = 0

or (x² – 4x) + (y² – 5y) = 45

Now completing the squares with in the parenthesis, we get

(x² – 4x + 4)+(y² –8y + 16) = 4 + 16 + 45

or (x - 2)² + (y – 4)² = 65

Therefore, the given circle has centre at (2, 4) and radius .