Let $A$ and $B$ be variable points on $x$-axis and $y$-axis respectively such that the line segment $AB$ is in the first quadrant and of a fixed length $2d$. Let $C$ be the mid-point of $AB$ and $P$ be a point such that
(a) $P$ and the origin are on the opposite sides of $AB$ and,
(b) $PC$ is a line segment of length $d$ which is perpendicular to $AB$.
Find the locus of $P$.