Question 437950
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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: (1,-5), (1,11)
 {{{(x-1)^2/a^2 + (y-3)^2/8^2 = 1}}}  C(1,3)
foci are along the major axis: need to determine that major axis
foci are (1,1), (1,5)  F = 2 {{{sqrt(64-60) = sqrt(4)}}} = 2
 {{{(x-1)^2/60 + (y-3)^2/64 = 1 }}} 
{{{drawing(300,300,  -15,15,-15,15,  arc(1,3,15.5,16),
 grid(1),
circle(1, 3,0.4),
circle(1, 1,0.4),
circle(1, 5,0.4),
line(1,-5,1,11),
graph( 300, 300, -15,15,-15,15))}}}