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4.5: The Hyperboloid
https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Celestial_Mechanics_(Tatum)/04%3A_Coordinate_Geometry_in_Three_Dimensions/4.05%3A_The_Hyperboloid
is a hyperbola, and $a$ is the semi transverse axis. (As described in Chapter 2, $c$ is the semi transverse axis of the conjugate hyperbola.) If this figure is rotated about the $z$ -axis through...is a hyperbola, and $a$ is the semi transverse axis. (As described in Chapter 2, $c$ is the semi transverse axis of the conjugate hyperbola.) If this figure is rotated about the $z$ -axis through $360^\circ$ , the surface swept out is a circular hyperboloid (or hyperboloid of revolution) of one sheet. If the figure is rotated about the $x$ -axis through $360^\circ$ , the surface swept out is a circular hyperboloid (or hyperboloid of revolution) of two sheets.

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