Equation of family of circle passing through two point #shorts

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

Obtain the differential equation of the family of circles passing through the point (a,0) and ca,0) .

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))

Equation of a circle passing through 3points

Equation of a family of circle passing through the extremities of the latus rectum of the parabola y^(2)=4ax , g being a parametric is

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

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