The parabola as a locus

In Year Two the parabola was the graph of $y = ax^2 + bx + c$, an object born from algebra. Here we redefine it in a purely geometric way, as the locus of the points equidistant from a focus and a directrix, and from this definition we derive the equation, the formulae for focus, vertex and directrix, and their proof.

• The parabola as a locus
• Parabola from focus and directrix
• Formulae for focus, vertex and directrix