Solution
= Solution
At a fixed observation time $t$, varying the release time $0<s<t$ gives
$$
x=t^2-s^2,\qquad y=\frac{x^2}{4}.
$$
Hence the dye <streakline> is the parabolic arc
$$
\boxed{y=\frac{x^2}{4},\qquad0<x<t^2}.
$$
= Solution
At a fixed observation time $t$, varying the release time $0<s<t$ gives
$$
x=t^2-s^2,\qquad y=\frac{x^2}{4}.
$$
Hence the dye <streakline> is the parabolic arc
$$
\boxed{y=\frac{x^2}{4},\qquad0<x<t^2}.
$$