Evolute/Examples/Parabola

Example of Evolute

Let $P$ be a parabola embedded in the Cartesian plane whose equation is given by:

$y^2 = 4 a x + 8 a^2$

The evolute of $P$ is the semicubical parabola whose equation is given by:

$4 x^3 = 27 a y^2$

Proof

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Sources

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