Recently, I learnt that other than using a quadratic equation to describe a parabola, it is also possible to say that a parabola is the locus of points that is equidistant from a focus and a directrix.
The idea of the parabola having points equidistant from a single focus and a line (directrix) seems like an acceptable idea, but for some reason,
I've been wondering how we know that this definition works? Is there a way to show that all the points are equidistant from the focus and directrix?