Maximum number of parabolas that can be drawn with a given directrix and tangent at vertex. If the equation of the directrix and tangent at the vertex is given then the maximum number of parabola , which can be drawn is. ? My approach is :- Since directrix can't be changed then only 1 parabola is possible.

If the directrix and the tangent line at the vertex are given but not the vertex, there exist infinitely many parabolas.
The vertex of such parabola is any point lying at this tangent line.
The width of all these parabolas is the same, because is uniquely determined by the distance between the two given lines ( they are parallel).