/sci/ - Science & Math

What’s the redpill on parabolas? When I was a youngster they simply taught us to think of parabolas as the graphs of polynomials of the 2nd degree, ax^2+bx+c

I am reading an older text and it introduces parabolas as the equation of points (x,y) such that each point is equidistant from the directrix and the focus. So with the focus being (0,p) and the directrix being y = -p we have x^2= 4py or y = x^2/4p

Is there any reason to choose one representation or the other?