In each of the following, find the centre and radius of the circles.
x2 + y2 – 4x – 8y – 45 = 0
The equation of the given circle is x2 + y2 – 4x – 8y – 45 = 0.
x2 + y2 – 4x – 8y – 45 = 0
(x2 – 4x) + (y2 -8y) =45
+ 
– 4 – 16 = 45
(x - 2)2 + (y – 4)2 =65
(x - 2)2 + (y – 4)2 =
, which is form (x-h)2 +(y-k)2 = r2, where h=2,
K= 4 and r=
Thus, the centre of the given circle is (2, 4), while its radius is
.
9