Evolute of a Parabola

Method 1
Using direct formula from [url=https://twitter.com/gregeganSF/status/1267616726436286464/photo/1]https://twitter.com/gregeganSF/status/1267616726436286464/photo/1[/url][br]by [url=https://twitter.com/gregeganSF]Greg Egan[/url][br][br][code]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) = 0[/code]
Method 2
Using GeoGebra's [url=https://wiki.geogebra.org/en/Envelope_Command]Envelope() Command[/url], adapted from [url=https://www.geogebra.org/m/xvddq4xq]https://www.geogebra.org/m/xvddq4xq[/url]

Information: Evolute of a Parabola