Question 444457
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Hi

Standard Form of an Equation of an Ellipse is {{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1 }}}
where Pt(h,k) is the center and a and b  are the respective vertices distances from center.
 endpoints of the major axis: (2,4),(2,12) 12-4 = 8/2 b = 4 Center( 2,8)
  {{{ (x-2)^2/a^2 + (y-8)^2/16 = 1}}}  
foci (2,5),(2,11)  f = 3  {{{sqrt(16-7) = sqrt(9) = 3}}}  a^2 = 7
    {{{ (x-2)^2/7 + (y-8)^2/16 = 1}}}  
{{{drawing(300,300,-20,20,-20,20, arc(2,8,5.3,8),
 grid(1),
circle(2, 8,0.4),
circle(2, 5,0.4),
circle(2,11,0.4),
graph( 300, 300,-20,20,-20,20))}}}