111)
Converting the entire thing into Co-ordinate Geometry, we have eqn of BM as x+y=1.
Meaning z is of the form h+i(1-h)
So If (x,y) be the point of u at some instant we have
x=h^2-(1-h)^2\\ \ y=2h(1-h)
h=\frac{x+1}{2}
Putting it in the 2nd eqn we have locus as
\boxed{ 2y=1-x^2} - which is that of a parabola.
