Lemniscate of Bernoulli from Tangents to Rectangular Hyperbola

Theorem

Let $\KK$ be a rectangular hyperbola.

Let $\LL$ be the locus of the foot of the perpendicular from the origin to the tangents to $\KK$.

Then $\LL$ is the lemniscate of Bernoulli.

Proof

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Sources

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