The locus of the centre of the circle for which one end of the diameter is (3,3) while the other end lies on the line x+y=4.
let (h,k) be the centre of the circle and other end of diameter be (x1,y1).
h= (x1+3)/2 and k= (y1+3)/2
or, x1=2h-3 and y1=2k-3
but (x1,y1) lie on x+y=4,
for locus, replace (h,k) by (x,y)..
thus, locus is x+y=5