Plane Section of Hyperboloid of Revolution Parallel to Axis of Rotation is Hyperbola

Theorem

Let $\HH$ be a hyperboloid of revolution.

Let $\SS$ be a plane section of $\HH$ taken parallel to the axis of rotation of $\HH$.

Then $\SS$ is a hyperbola.

Proof

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Also see

• Cross-Section of Hyperboloid of Revolution is Circle

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hyperboloid
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hyperboloid