SOLUTION: find an equation of the ellipse having a major axis of length 12 and foci at (1,2) and (-3,2)

We plot the foci (1,2) and (-3,2). 

Then we plot the center which is the midpoint between the two foci,
which is (-1,2). Then we draw the major axis 12 units long,
with the center at the middle, which means that we draw it 6 units 
on each side of the focus (in green).  That means that the vertices are 
(-7,2) and (5,2). 



We know that this ellipse looks like this:.

Therefore its equation is 



The center is (h,k) = (-1,2).
We know that "a" = half the major axis = half of 12 = 6

So we can fill in h,k, and a:




We only need b, the semi-minor axis:



We calculate b from 
                    
                    
                    
                    
                    
                    , approximately 5.7 units
                    up and down from the center. 

So the equation is 

  
                   
It looks like a circle but I'll draw a circle (in red) so you
can see that it's not quite a circle:


 
Edwin