Put the equation of the ellipse in standard form. The standard form is
(x-h)^2/r1^2 + (y-v)^2/r2^2 = 1.
For example, if the equation is ((x-2)^2 / 9) + ((y-1)^2 / 4) = 4 you would divide each side by 4 to get ((x-2)^2 / 36) + ((y-1)^2 / 16) = 1. You would further manipulate that equation by expressing the denominators as squares, ending up with:
((x-2)^2 / 6^2) + ((y-1)^2 / 4^2) = 1.
Inspect the equation to identify the different components of the equation.
For the example problem, h is 2, v is 1, r1 is 6, and r2 is 4.
Use the ellipse parameters to mark key points on the graph. The center of the ellipse is at (h,v) and the horizontal edges of the ellipse are at (h + r1, v) and (h - r1, v) and the vertical edges are at (h, v + r2) and (h, v - r2).
For the example, the center is at (2,1), the horizontal edges at (-4, 1) and (8, 1), the vertical edges at (2, -3) and (2, 5).
Smoothly connect the edges in a symmetric, oval shape. You have graphed the ellipse.