# Find a projective change of coordinates

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 $$y^2=2pxz$$)

• Essentially a duplicate of math.stackexchange.com/q/1273662/265466. – amd Jan 8 at 2:33
• I don’t get the explanation there, it becomes the regular circumference, not its completion. – M. Navarro Jan 8 at 7:47
• 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. – Maxim Apr 14 at 13:27