Find the locus of a point which moves such that its distance from the line y = 4 is a constant

A predator moves in a circle of radius $\sqrt{2}$centre (0,0), while a prey moves along  y = x. If $0\le x\le 2$, at which point will they meet

P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight ST is on the locus of P and $\angle VUS={{50}^{o}}$ find $\angle UST$

If P and Q are fixed and X is a point which moves so that XP = XQ. The locus of X is