A circle is centered at [0,0] with radius R. A parabolic arc is defined by a point P, a velocity vector v and an acceleration vector a. The entire arc is considered; the point chosen is arbitrary. Find all points of intersection.

I understand this problem is solvable by a quartic equation, but is there any simpler way?

  • $\begingroup$ Should be quadratic... no? $\endgroup$ Oct 3, 2019 at 16:33
  • 1
    $\begingroup$ @David You end up with a system of quadratic equations, but when you do the logical substitution you end up squaring the square so you have a quartic. $\endgroup$ Oct 3, 2019 at 16:39
  • $\begingroup$ Instead of parametrizing the parabola and plugging that into the equation of the circle, try parametrizing the circle and plugging that into the equation for the parabola. You will still get a quartic, but in cosine and sine, which have all sorts of nice properties lying around, handy for reducing the degree of the expression. I haven't tried it, but it might be workable. $\endgroup$ Oct 4, 2019 at 3:43


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