Geometry: Equation of a Circle

Worked Solution:

The circle with centre at ( 0, 0 ) and radius r has equation x² + y² = r².
Replacing x by x – a and y by y – b moves the centre to (a, b):
(x – a)² + (y – b)² = r²
x² – 2 a x + y² – 2 b y + a² + b² – r² = 0
So the centre is found from the x and y coefficients in the circle's equation:
–2 a = –6, the coefficient of x
–2 b = –4, the coefficient of y
so the centre is (a, b) = (3, 2).
The constant in the circle's equation is 5 = a² + b² – r² = 3² + 2² – r² = 13 – r²
r = √8 = 2.828 to 3 dps.