# Geo4.76

From Example Problems

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

or

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