Family of Circles
A family of circles are said to be concentric if they have the same centre but different value of their radii.
So, let is the general equation of the circle centred at
represents the equation of family of circles centred at and varying radius.
Problem Solving Trick
The equation of all concentric circles differ by a constant.
Equation of Circle Through the Intersection of Line and a Circle
Let is the equation of the line
and is the general equation of the circle then the equation of circles(s) passing through the point of intersection of line and circle is/are given by the equation.
where,λ is a constant and the value of λ can be obtained from some other given conditions.
Equation of Circle Through the Intersection of two Circles
are the general equation of circle the circle passing through the point of circle s1 and s2 is/are represented by the equation
where, is a constant and the value of can be obtained from some other given conditions.