BodhiAI

Nov. 13, 2019

**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 s_{1} and s_{2} is/are represented by the equation

** **

** **

** **

** **

**where, is a constant and the value of can be obtained from some other given conditions.**