I assume that you are familiar with the material of the lesson  Ellipse definition, canonical equation, characteristic points and elements 
in this site. Surely, you may learn it from other sources. But if you are not familiar with it, I recommend you to read this lesson.

Notice that the center (3,0) and the focus (3,4) of our ellipse lie in one vertical line, and the distance 
between the center and the focus is 4 units. This distance is half of the ellipse's focal distance. 
Its standard notation is "c" and the standard name is "linear eccentricity".

So, we have the minor semi-axis b = 4 and the linear eccentricity c = 4.

Then the major semi-axis a =  =  = .

Since the ellipse's foci lie in the vertical line, semi-major axis "a" relates to the vertical coordinate "y", 
while the semi-minor axis "b" relates to the horizontal coordinate "x".

Thus the standard equation of our ellipse is 

 +  = 1,   or    +  = 1.