The origin is a limiting point of a system of coaxal circles of which is a member.Show that the equations of the circles of the orthogonal system are for different values of k.
Given a member of a coaxal system and (0,0) is a limiting point.
Therefore,the limting point circle equation is
The equation to the radical axis is
Any circle of the coaxal system is
Let the equation of the circle cutting the system of coaxal circles orthogonally be
. the equation be 2.
The circle 2 passes through the limiting points of the coaxal system, then we have d=0.
Therefore, the euquation to the orthogonal system is
for different values of k.