There are two cases.

Case 1.  If the hyperbola has equation ,

then for p < a,  any ellipse whose equation is
will share the vertices (h+a,k) and (h-a,k) and the center (h,k).

Case 2.  If the hyperbola has equation ,

then for p < a,  any ellipse whose equation is
will share the vertices (h,k+a) and (h,k-a) and the center (h,k). 

Example and graph for case 1.

 <-- hyperbola
 <-- ellipse



Example and graph for case 2.

 <-- hyperbola
 <-- ellipse



Edwin