Question 955294
The foci allow finding the center, and then that one given vertex lets you know value for variable a.


CENTER:  On line x=4, y value is {{{(2+8)/2=5}}}.


Note that foci are in a vertical arrangement so "a" goes under the y-rational expression.  {{{a=10-5=5}}}.


Currently we have a=5 and  {{{highlight_green((x-4)^2/b^2+(y-5)^2/(5^2)=1)}}}.


{{{a^2=b^2+c^2}}}, from the graph and derivation of an ellipse with vertical axis of symmetry or either horizontal axis of symmetry.
How far is center from either focus?  {{{3=c}}}.
What was a?   {{{a=5}}}.
Find b.
{{{b^2=a^2-c^2}}}
{{{b^2=25-9}}}
{{{b^2=16}}}
{{{b=4}}}


Finish the equation:
{{{highlight((x-4)^2/4^2+(y-5)^2/(5^2)=1)}}}