In geometries named for this figure, there are multiple lines parallel to a given line through a given noncollinear point.
In geometries named for this figure, there are multiple lines parallel to a given line through a given noncollinear point. The orbit of unbound comets takes this shape, and the three-dimensional analogues of this conic section can be of one or two sheets. Formally defined as the locus of points the (*) difference of whose distances to two foci (FOH-sai) is a constant and exemplified by the graph of y equals one over x, name this conic section with a eccentricity greater than one and two separate branches.
In geometries named for this figure, there are multiple lines parallel to a given line through a given noncollinear point.
{hyperbola}s [or {hyperbolic}; accept {hyperboloid}s; prompt on {non- Euclidean} geometries before "shape"; accept {Lobachevsky}/ian geometries before "shape"]