Evolute of a Parabola
Method 1
Using direct formula from https://twitter.com/gregeganSF/status/1267616726436286464/photo/1
by Greg Egan
16a⁴ x⁶ - 8y³ (4a³ d² + a) - (4a² d³ + d)² + 16a² y⁴ + y² (1 - 4a² d²)² + 8a d² y (4a² d² + 1) + x² (-32a³ y³ + y (8a³ d² - 2a) + 4a² d² (12a² d² - 5) - 32a² y² (a² d² - 1)) + x⁴ (-48a⁴ d² + 16a⁴ y² - 40a³ y + a²) = 0Method 2
Using GeoGebra's Envelope() Command, adapted from https://www.geogebra.org/m/xvddq4xq