If it's an ellipse that looks like this , its equation is



If it's an ellipse that looks like this , its equation is



We plot the three given points, and connect the center to the given
focus in red, for that is the value of "c". Since the given point 
(4,7) on the ellipse has the same x-coordinate as the center, that
point has to be the covertex, so we connect the center to it also,
in green, for that is the value of "b", the semi-minor axis. 



We see that the ellipse has the equation



And that the center (h,k) = (4,6), and c = 5 because the red line is
5 units long.  The other focus has to be 5 units to the left of the 
center, which is (-1,6).  We can calculate the value of "a", by using 
the relationship between a,b, and c for ellipses: 



  
 


That's about 5.1. So it's equation is



we sketch in the ellipse:



Edwin