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BodhiAI
Nov. 13, 2019

Family OF Circle:

 

Family of Circles

Concentric 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.

i.e.,

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

Let

and

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.