I think you need a more graphical approach than just a word explanation.

Plot the points and draw the graph:



Since the ellipse is this way "" and not this way "", its equation is:

    +  = 1

[Had it been the other way the "a" and "b" would be switched. In an
ellipse "a" is always larger than "b", but not necessarily in a hyperbola!]

(h,k) = the center = (3,2),  "a" = semi-major-axis, sometimes called
"the long radius" and "b" = the semi-minor-axis, sometimes called
"the short radius".

draw the semi-major and semi-minor axes:
The red line is the semi-major axis and the green line is the semi-minor
axis.



Count the number of units that the red and green lines are in
length and you'll get a = 6 and b = 3.  Therefore the equation

 +  = 1

becomes:

 +  = 1

or

 +  = 1

Edwin