Parallel to a Parabola

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I received a question today about what curve is parallel to a parabola. I sat for a minute and realized that it wasn’t another parabola. It required parametric equations (at least if you wanted to keep it simple). That of course lead to code:

See the Pen jOqzMJb by Sophia (@fractalkitty) on CodePen.

The parametric equations for the parabola are:

  • x = 2at
  • y = at2

The parallel curve equations are:

  • x = 2at+ct/sqrt(1+t2)
  • y = at2 – c/sqrt(1+t2)

2 responses to “Parallel to a Parabola”

  1. shaunakde Avatar

    This is so cool!

    1. fractalkitty Avatar

      Thank you 🙂

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