Find the locus of the poles of the line w.r.t the circles which touch the coordinate axes and whose centre lies in the first quadrant.
Given line is
Equation of any circle which touches the coordinate axes and whose centre lies in the first quadrant is
Let P(x1,y1) be the pole of the line w.r.t the above circle, hence polar w.r.t. circle is
Let this equation be 3.
since the first one and the 3 both represent polar of P w.r.t the circle
From two of the above,
Taking the second two equalities,
Substituting the value of lambda in this equation, we get
Therefore, the required locus of P is