Parabola Equation from its trajectory points in a Video

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I have a video of an object describing a ballistic trajectory (i.e. A ball being thrown) The video is filmed with an angle and not orthogonally to the moving object, the camera is calibrated.

I am able to register the ball centres along the frames and extract the trajectory points.

Knowing all points and that the trajectory is a parabola, is there a way to recover the parabola plane and its equation?