Question 867576
Find the equation of the ellipse with foci (2,-4) and (2,8) and with a vertex at (2,10) . 
***
Given data shows ellipse has a vertical major axis. (y-coordinates of foci change but x-coordinates do not)
Its standard form of equation: {{{(x-h)^2/b^2+(y-k)^2/a^2=1}}}, a>b, (h,k)=coordinates of center
For given ellipse:
y-coordinate of center=2(midpoint between -4 and 8)
x-coordinate of center=2
center:(2,2)
a=8 (distance from center to vertex on the vertical major axis)
a^2=64
c=6  (distance from center to foci on the vertical major axis)
c^2=36
c^2=a^2-b^2
b^2=a^2-c^2=64-36=28
Equation:  {{{(x-2)^2/28+(y-2)^2/64=1}}}