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|.
The equations of the required circle are