Asymptote to Strophoid

Theorem

Let $S$ be a strophoid embedded in a Cartesian plane with the equation $y^2 = x^2 \dfrac {x + a} {a - x}$.

Then the straight line $x = a$ is an asymptote to $S$.

Proof

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Sources

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