Cabri has a built in method for constructing the unique conic through five points. 

focus, directrix and point  Classically, a conic C is defined in terms of a line D, the directrix,
a point F, the focus, and a positive number e,
the eccentricity. In fact, C is the locus
where PD denotes the distance of the point P from the line D.
This construction can be implemented in Cabri,
but it is easier to define the eccentricity implicitly by giving a particular point on the conic.

parabola  For a parabola, the eccentricity is 1, so we can specify it by just the focus and directrix.

central conic  Just as there is a unique conic through five points, there is a unique central conic (ellipse or hyperbola) through three points. 
five lines  Just as there is a unique conic through five points (with no three in a line), there is a unique conic touching five lines (with no three concurrent or parallel). This is of course the dual property. 
Main Cabri Page  Conics Pages  Classical Theorems 