Polar Equation of Conchoid of Nicomedes

Theorem

Let $a \in \R$, $b \in \R_{>0}$ be real constants.

Let the focus point of a conchoid of Nicomedes $\KK$ be located at the origin of a polar plane.

Let the directrix of $\KK$ be the straight line through $\polar {a, 0}$ perpendicular to the polar axis.

Then $\KK$ can be expressed in polar coordinates as:

$r = b + a \sec \theta$

Proof

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Also see

• Cartesian Equation of Conchoid of Nicomedes

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): conchoid
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): conchoid
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): conchoid

• Weisstein, Eric W. "Conchoid of Nicomedes." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConchoidofNicomedes.html