Critical attributes for graphing an ellipse are: **center**, **length of major radius**, **length of minor radius**, and **length of focal radius**.

Here is an example of sketching the graph of an ellipse using
x minus two squared over four
(*x* − 2)^{2}
4
+
y plus three squared over sixteen
(*y* + 3)^{2}
16
= 1.

Center (2, -3), major radius (y-direction) = 4, minor radius (x-direction) = 2.

Focal radius^{2} = 4^{2} – 2^{2} = 16 – 4 = 12. So focal radius = units.

** Step 1**: Locate and plot the center point.

**Step 2**: Locate and plot points on major axis 6 units from center in either direction and on minor axis 4 units from center in either direction, as shown in the following figure.

**Step 3**: Sketch in the curve of the ellipse through the four points on the major and minor axes as shown in the figure below.

*Notice the major axis of this ellipse is vertical because the radius in the y-direction is the longer.*