In these illustrations, the blue space triangle's horizontal side is c, 
The other sides r1 and r2.  (r1+r2) remains constant as does c.
The corner where r1 and r2 meet is a focus F of the two green ellipses.

Both ellipses have semimajor axis a, which remains constant.
When F becomes colinear with c,
both the green ellipses become rectilinear ellipses with eccentricity 1.