It follows from the Conicoid equation that a solution exists only for . For , there is no solution with . The form of conicoid is displayed on fig.1. For , conicoid sections with planes have the form of ellipses with the formula (fig.2). The center of the ellipse is located on the axis Y. The small axis is directed along Z and has a length of . The large axis of the ellipses is directed along the X axis and has a length of . The formula for this section in the new notations takes on a canonical form of ellipses . The conicoid body takes on values within.
The section by has the equation which is a parabola with an axis of symmetry parallel with axis Y. The canonical form of the parabola is , where , and is its vertex. The vertex moves out of plane XZ as c increases. All the sections are simalar to each other with the focus distance of parabola . Due to symmetry about YZ plane for we get exactly the same cross sections.
fig.1
fig.2
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