Given a rectangle $ABCD$ with $A=(0,0), B=(t,0), C=(t,1)$ and $D=(0,1)$ for $0<t<\infty$ , let $P$ be the intersection of the diagonal $BD$ with the perpendicular to this diagonal by $C$. The locus of $P$ as $t$ varies is the curve $yx^2=(1-y)^3$. I'm looking for info on this curve (hoping that someone has already dealt with it!), be it historical (is it a well-known curve?) or as related to other geometrical loci. Thanks in advance for your help.
The curve you describe is a specific case of a Cissoid of Diocles. Yours is rotated but the shape is the same.