View source for Bicylindrics

Two closed curves obtained as the intersection of two cylinders the axes of which intersect at right angles. The parametric equations of bicylindrics are

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016140/b0161401.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016140/b0161402.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016140/b0161403.png" /> are the radii of the cylinders and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016140/b0161404.png" /> is a parameter. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016140/b0161405.png" />, the bicylindrics is a pair of congruent ellipses.