Maths circle LQ, difficult

Given that circle C has the equation of x^2 + y^2 - 6x - 6y + 10 = 0

So, the coordinates of center are (3,3)

Line L1 touches circle C at A(1,1) and its equation is y = 2 - x

Now,
Line L2 is drawn to touch circle C at point B(m,n) and cuts the y-axis at the same point as line L1 does.

Find, by using (a)differentiation and (b)any methods other than differentiation :
(i) the equation of line L2
(ii) the values of m and n
(iii) if point P(h,k) moves such that PA is perpendicular to PB, find the equation of locus of point P