Find the equation of a circle with centre (2,2) and passes through the point (4,5).

Since the centre is (2, 2)

We have (x – 2)² + (y – 2)² = r²

This circle passes through the point (4, 5)

(4 – 2)² + (5 – 2)² = r²

or 4 + 9 = r²

or r² = 13

The required equation of the circle is
(x – 2)² + (y – 2)² = 13

or x² – 4x + 4 + y² – 4y + 4 = 13

or ; x² + y² – 4x – 4y - 5 = 0.