examday

/TMUA

The point $A$ lies on the $x$-axis with non-negative $x$-coordinate, and the point $B$ lies on the $y$-axis with non-negative $y$-coordinate. The length $AB$ is $6$.

The point $P$ lies on the line segment $AB$, with $AP:PB=1:2$. As $A$ and $B$ vary, $P$ traces a curve.

What is the area, to the right of $x=2$, bounded by this curve, the $x$-axis and the line $x=2$?

One possible position of the segment is shown.