The other tutors don't draw graphs.  But you can never 
learn conics if you don't draw graphs.  

Draw the foci which are given as (-1,1) and (5,1):



1. Plot the foci (-1,1) and (5,1).

This tells us that we have an ellipse like this , which has equation



The center (h,k) is the midpoint between the two foci which is (2,1),
We plot that.



So we can fill in h and k in the equation h=2, k=1.



Now we draw the major axis which is 8 units long, with its center
bisecting it, so it is 4 units to the right of the center and 4
units left of the senter.  So we draw the major axis in green:



We know that a is the length of the semi-major axis or half of the major
axis, so a=4, and we can fill in a=4 in the equation



Ther vertices are the endpoints of the major axis, so they are (-2,1) and
(6,1). We plot those:

 

Next we calculate b, the length of the semi-minor axis from the equation:
"c" is the distance from the focus to the center, which is 3 units.







, about 2.65, and the center bisects the minor axis also.
so we draw in the minor axis also, about 2.65 up from the center, and
2.65 down from the center, like this:



And finally we can draw in the graph of the ellipse:



Since we now know that , the equation is now:



or



Edwin