Graphing the general picture of an ellipse given an equation is relatively simple work. It's all about interpretation.
Let's start by looking at our standard ellipse equations:
#(x-h)^2/a^2+(y-k)^2/b^2# (Horizontal Ellipse)
#(x-h)^2/b^2+(y-k)^2/a^2# (Vertical Ellipse)
#a# and #b# simply describe the distance from the centre that the ellipse goes.
The one under #x# is the distance it travels vertically, while the one under #y# is the distance it travels horizontally. Do not be intimidated by the #b# and #a#; they simply tell you which one is longer (#a# is always longer than #b#).
Also, #h# and #k# give you the coordinates for your vertex. #(h, k)# is your vertex.
Now all you need to do is take your centre, and measure out #a# and #b# distance in the appropriate directions, connect the dots, and you are done. Just make sure that you square root your #a# and #b# before using them, and that you're using them in the right direction (#x# or #y#). Also watch out for the signs of your #h# and #k#.
Hope that helped :)
