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,

(2h-3)+(2k-3)=4

or, h+k=5

for locus, replace (h,k) by (x,y)..

thus, locus is  x+y=5

Approved