The bic-II stationary-locus criterion for conic loci of triangle centers

Let $X$ be a triangle center that does not always lie on a triangle's circumcircle. Consider the bic-II family and its bic-I (poristic) subfamily. A locus is stationary when the corresponding triangle center remains fixed over the poristic family. The bic-II stationary-locus criterion. Over the bic-II family, a necessary (though not sufficient) condition for the locus of $X$ to be a conic is that its locus over the bic-I (poristic) family is a stationary point. This is an experimental necessary condition relating conic loci in the bic-II family to stationary triangle centers in the poristic case; sufficiency is explicitly not claimed, and no resolution is given here.