0
The equation of a circle with its centre at C(x0, y0) and radius r is:
(x – x0)2 + (y – y0)2 = r2
If x = y0 = 0 (i.e. the centre of the circle is at origin) then equation of the circle reduce to x2 + y2 = r2.
If r = 0 then the circle represents a point or a point circle.
The equation x2 + y2 + 2gx + 2fy + c = 0 is the general equation of a circle with centre
(–g, –f) and radius √(g2+f2-c).
Equation of the circle with points P(x1, y1) and Q(x2, y2) as extremities of a diameter is
(x – x1) (x – x2) + (y – y1)(y – y2) = 0.
For general circle, the equation of the chord is x1x + y1y + g(x1 + x) + f(y1 +y) + c = 0
For circle x2 + y2 = a2, the equation of the chord is x1x + y1y = a2
