Find the length of Latus Rectum of the Parabola 169{(x-1)2 +(y-3)2 }=(5x-12y+17)2

as parabola is locus of point which moves in such a way that its distance from a fixed point (focus) and from a fixed line (directrix) is constant  here focus is (1,3) and directrix is 5x-12y+17 = 0     from point (1,3) length of perpendicular to directrix is half the length of latus rectum. 

length of perpendicular is  (5*1 -12*3 +17) /  (5² + 12²)  =  14/13  so length of latus rectum is  28/13