Tips for graphing an ellipse.
The equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1 for an ellipse that is elongated along the x-axis.
The longer axis of the ellipse is the major axis and is of length 2a. The shorter axis of the ellipse is the minor axis and is of length 2b.
Plot the coordinate of the center (h,k) and move "a" units in each direction from the center along the major axis. Move "b" units from the center in each direction along the minor axis. These 4 points are the vertices. Then draw a smooth curve through the 4 points.
If you want to plot the foci, you need a value for c, which is found by c^2 = a^2 - b^2. Move c units from the center along the major axis in both directions and plot the point.