General equation of a circle:
The general equation of circle is of the form x2 + y2 + 2gx + 2fy + c = 0 here g, f and c are constants. The given equation of the circle in the standard form can be given as 
. Thus the coordinates of its centre are (-g, -f) and radius is 
.
Case I: if
>0, a real circle is possible.
Case II: if =0, the circle is called a point circle.
Case III: if < 0 no real circle is possible.
Working rule to find out the centre and radius of the circle whose equation is given:
STEP I: Make the coefficients of x2 and y2 equal to 1 and right hand side equal
to zero.
STEP II: The coordinate of the centre will be (a, b) here a= -1/2 (coefficient of x)
and b= 1/2 (coefficient of y).
STEP III: 
Illustration:Find the centre and radius of circle
(A) 2x2+2y2-4x-5y-1=0.
(B) 
for some λ.
Solution: (A) The given equation of circle can be written as x2+y2-2x-5/2y-1/2=0
=>g=-1, f=-5/4 c=-1/2
Thus the centre is (1,5/4) and radius is 
.
(B) The given equation can be given as
As there is no term of xy in the equation of circle =>λ = 0
Thus the given equation reduces to x2+y2-x+2y-2=0. Centre is (1/2, -1) and radius is √13/2
Parametric equation of a circle:
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Let equation of circle be (x - a)2 + (y - b)2 = r2. Hence from the diagram it is clear that co-ordinates of any point on the circle can be taken as (a + r cosq, b + r sinq) where 0 ≤ q < 2Π .
x = a + r cosθ and y = b + r sinθ is called as parameter equation of the circle.
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