Property 1: The equation of the family of circles passing through the point of intersection of two given circles .

Property 2: The equation of the family of circles passing through the point of intersection of line and circle

The equation of the circle passing through the point (1,1)

The equation of any circle passing through the points of intersection of the circle S=0 and the line L=0 is

Equation of a circle passing through 3points

Statement 1 : The equation x^2+y^2-2x-2a y-8=0 represents, for different values of a , a system of circles passing through two fixed points lying on the x-axis. Statement 2 : S=0 is a circle and L=0 is a straight line. Then S+lambdaL=0 represents the family of circles passing through the points of intersection of the circle and the straight line (where lambda is an arbitrary parameter).

Property 3: The equation of the family of circles touching the circles and line at their point of contact is

What is the number of circles passing through a given pair of points ?

The differential equation of the family of circles passing through the origin and having centres on the x-axis is :

Property 4: The equation of the family of circles passing through two given points P(x_(1),y_(1)) and Q(x_(2),y_(2))