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Two boats, $A$ and $B$ , are moving on still, open water. Relative to a lighthouse positioned at the point $(0, 0)$ , the positions of the boats at time $t$ are given by

A = (2 t + 1, t - 2)

and

B = (t - 1, 2 t)

Find the time at which $A$ is equidistant from the lighthouse and $B$ .
Find the distance from $A$ to the lighthouse at this time.

The distance from $A$ to the lighthouse can be found using the distance formula on

(0, 0) and (2 t + 1, t - 2)

The distance from $A$ to $B$ can be found using the distance formula on

(t - 1, 2 t) and (2 t + 1, t - 2)

Equidistant means the two distances must be equal.