We must get that in standard form, which is:

 if the ellipse looks like this: ,

or  if the ellipse looks like this: ,

Where the length of the major axis is  and the length of
the minor axis is .




All the completing of the square and factoring has already been done, so
we can start by getting a 1 on the right. To do that, we divide through
by 36:



Simplifying,



Since 9 is greater than 4 it is of the form:

 so the ellipse looks like this: ,

Therefore  and .

The major axis is  or  or 

Here is the graph.  The ellipse's center is at (-4,1).

Its major axis is the green line which we see is 6 units long.



Edwin