Given that arg((z-1)/(z-2i)) = pi/4 describe the locus of P and sketch this on an argand diagram. Show that the point (1,3) lies on this locus.

Question

I know it is an arc subtended from the points (0,2) and (1,0) but I do not know how to find the centre of the circle which I am guessing is how I would go on to draw the diagram accurately and answer the second part about the point (1,3)