A generic plane containing the x axis (Ox) has a unit normal vector
Two vectors (unit and mutually perpendicular) that span this plane are
Hence, on this plane, the position vector of any point is where is the coordinate vector of r with respect to .
Plug this into the equation of the hyperbolic paraboloid,
which is an equation of hyperbola in . If the semi-axes are equal then
Hence, the required angle satisfies
This determines four possible values for and correspondingly four planes.
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