1. Draw two circles with radii and , equal to the semimajor and semiminor axes of the ellipse.

2. Draw a radial line from the center, at an angle from the horizontal, that intersects the two circles at points and .

3. Drop a line from to the horizontal axis (shown in blue).

4. Draw a line from the vertical axis through point to intersect this line (shown in green).

5. The intersection represents a point on the ellipse. To trace the ellipse, repeat steps 2 to 4 for different angles .

This construction reproduces the standard parametric trigonometric representation of an ellipse: .