I'm sorry for the stupid question, but it seems that extensive googling didn't yield an answer.
I've learned about parabolas, and how the parabola is the curve that is equidistant from a point (Focus) and a line that is perpendicular to the axis of the parabola.
But then, while studying classical mechanics, you come upon the fact that a projectile follows a parabolic path! And it seems that the only justification i can find for it is that since the path of the projectile is given by a quadratic function, it's curve is a parabola.
However, i can't seem to find a proof that the curve of quadratic function is the curve given by the set of points equidistant from a particular point and a line.