# Geo4.135

From Example Problems

Show that as k varies the circles form coaxal system.Find the radical axis.

Given circles are . Equation 1

Two members of the family are

Let these be 2 and 3

(2)-(3) gives

Equation 1 represents a system of coaxal circles whose radical axis is

It can be written as

Let cut this circle orthogonally,

Therefore

Simplifying this equation, we have

If this is true for all values of k, then we have

Solving

Therefore, the system of circles orthogonal to (1) is