# Geo4.37

From Example Problems

Find the equations of circles which touch the axis of x at the origin and the line

Let the equation of the required circle is

Let the equation to the tangent at the origin (0,0) to the above be gx+fy+c=0

Given the tangent at(0,0) is x axis i.e y=0,means g=0,c=0

From the first one and just the above one,we have

Given that this equation touches the line

Perpendicular distance from (0,-f) on the above line is radius |f|.

Hence

This gives

The equations of the required circle are