The distance between the polar of (P(2,3) ) with respect to the circle (x^2+y^2-2 x-2 y+1=0 ) and the polar of the inverse point of (P ) with respect to the same circle is

Step-by-step solution

Equation of polar of point (P(2,3) ) with respect to the circle (x^2+y^2-2 x-2 y+1=0 ) is ( aligned & T=0 2 x+3 y-(x+2)-(y+3)+1=0 & x+2 y-4=0 (i) aligned ) End equation of line joining of points (P(2,3) ) and centre of the given circle (C(1,1) ) is (y-1= 2 1 (x-1) 2 x-y-1=0 (ii) ) ( ) Inverse point of (P ) with respect to the given circle is point of intersection of polar Eq. (i) and line CP, Eq. (ii), so coordinate of the inverse point is (Q ( 6 5 , 7 5 ) . ) Now, equation of polar of point (Q ( 6 5 , 7 5 ) ) with