Question 731956
Thanks for clearing (some of) this information.  The more complete response is in your earlier post on this question.   We could not finish showing your "b" because the focus given was uncertain.  In fact, what you give in THIS posting #731956 is still wrong.  


If your vertices are (0, -1) and (12, -1) then your foci MUST have the SAME y coordinate of y=-1.  So, is one of your given foci really (6+11^(1/2), -1)?  


The center of your ellipse, assuming the given vertices are on the major axis, is (6, -1).  a=6, and c=6+11^0.5, so {{{b^2=6^2-(6+11^(1/2))^2}}}.