Find a projective change of coordinates that takes the projective completion of the circumference C: $x^2 + y^2 = 1$ to the projective completion of the parabola P: $y^2=2px$, $p \geq 0$

(i.e. $x^2 + y^2 = z^2$ to $y^2=2pxz$)

  • $\begingroup$ Essentially a duplicate of math.stackexchange.com/q/1273662/265466. $\endgroup$ – amd Jan 8 at 2:33
  • $\begingroup$ I don’t get the explanation there, it becomes the regular circumference, not its completion. $\endgroup$ – M. Navarro Jan 8 at 7:47
  • $\begingroup$ It's a change of variables in homogeneous coordinates. You can find the point on the circle that corresponds to the point at infinity $(1, 0, 0)$ on the parabola. $\endgroup$ – Maxim Apr 14 at 13:27

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