page_title: Elliptic cylindrical coordinates
hierarchical_section_title: Elliptic cylindrical coordinates
caption_attribution_description: Coordinate surfaces of elliptic cylindrical coordinates.
context_page_description: Elliptic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional elliptic coordinate system in the
  perpendicular -direction. Hence, the coordinate surfaces are prisms of confocal ellipses and hyperbolae. The two foci
  and are generally taken to be fixed at and
  , respectively, on the -axis of the Cartesian coordinate system.
context_section_description: Elliptic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional elliptic coordinate system in the
  perpendicular -direction.  Hence, the coordinate surfaces are prisms of confocal ellipses and hyperbolae.  The two foci 
   and  are generally taken to be fixed at  and
  , respectively, on the -axis of the Cartesian coordinate system.
caption: Coordinate surfaces of elliptic cylindrical coordinates.  The yellow sheet is the prism of a half-hyperbola corresponding to ν=-45°, whereas the red tube is an elliptical prism corresponding to μ=1.  The blue sheet corresponds to z=1.  The three surfaces intersect at the point P (shown as a black sphere) with Cartesian coordinates roughly (2.182, -1.661, 1.0).  The foci of the ellipse and hyperbola lie at x = ±2.0.
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