Editing Ellipse (section)

=== de La Hire's point construction ===
The following construction of single points of an ellipse is due to [[Philippe de La Hire|de La Hire]].<ref>K. Strubecker: ''Vorlesungen über Darstellende Geometrie.'' Vandenhoeck & Ruprecht, Göttingen 1967, S. 26.</ref>  It is based on the [[#Standard parametric representation|standard parametric representation]] <math>(a\cos t,\, b\sin t)</math> of an ellipse:
# Draw the two ''circles'' centered at the center of the ellipse with radii <math>a,b</math> and the axes of the ellipse.
# Draw a ''line through the center'', which intersects the two circles at point <math>A</math> and <math>B</math>, respectively.
# Draw a ''line'' through <math>A</math> that is parallel to the minor axis and a ''line'' through <math>B</math> that is parallel to the major axis. These lines meet at an ellipse point <math>P</math> (see diagram).
# Repeat steps (2) and (3) with different lines through the center.
<gallery widths="220" heights="220" class="float-left">
Elliko-sk.svg|de La Hire's method
Parametric ellipse.gif|Animation of the method
</gallery>

[[File:Elliko-g.svg|250px|thumb|Ellipse: gardener's method]]