Introduction
Circles of Class 11
Certain Forms of the Equations of circles
(a) Centre (h, k) and radius r
The equation is (x – h)2 + (y - k)2 = r2 (1)
(b) General form of the equation of a circle is
x2 + y2 + 2gx + 2fy + c = 0 (2)
If we compare equation (1) and (2) we get the centre of (2) as (-g, -f) and radius = 
(c) Equation of a circle on the segment joining (x1, y1) and (x2, y2) as the ends of a diameter is given by (x – x1)(x – x2) + (y – y1)(y – y2) = 0 (3)
(d) General equation of a circle which passes through A(x1, y1) and B(x2, y2) may be written as
(x – x1)(x – x2) + (y – y1)( y – y2) + λ
(4)
(e) The equation of the circle through 3 non-collinear points A(x1, y1), B(x2, y2) and C(x3, y3) is
= 0
Position of a Point
The point P(x1, y1) lies outside or inside the circle
S = x2 + y2 + 2gx + 2fy + c = 0 according as
S1 = 
> or < 0
