Equation of Cissoid of Diocles/Cartesian Form/Also presented as

Equation of Cissoid of Diocles in Cartesian Form: Also presented as

The Cartesian equation for the cissoid of Diocles can also be defined as:

$y^2 = \dfrac {x^3} {2 a - x}$

or:

$y^2 \paren {2 a - x} = x^3$

which can be derived directly from the form given by subtracting $x y^2$ from both sides and rearranging.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 11$: Special Plane Curves: Cissoid of Diocles: $11.33$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): cissoid
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cissoid
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cissoid

• Weisstein, Eric W. "Cissoid of Diocles." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CissoidofDiocles.html