Question 1000242
Difficult to make the right kind of drawing here, but try making a sketch of the ellipse as described.



Distance from center (8,2) to a vertex (13,2) is {{{A=13-8=5}}}, so {{{highlight(A=5)}}}.


Use the variable C as the distance from the center to either focus.  Your exercise description
will mean that you have C=3.


You want to find B.  The fact relating A, B, and C using C as the distance from center
to either focus, is {{{B^2+C^2=A^2}}}, giving {{{B^2=A^2-C2}}}.
Evaluate the value for B^2.
-
{{{B^2=A^2-C^2}}}
{{{B^2=5^2-3^2}}}
{{{B^2=25-9}}}
{{{highlight(B^2=16)}}}


The standard form equation {{{(Y-k)^2/B^2+(X-h)^2/A^2=1}}}  can now be filled-in, giving you
{{{highlight(highlight((X-8)^2/25+(Y-2)^2/16=1))}}}.