Derive parabola equation

What you'll learn

1. Define a parabola as the locus of points equidistant from a fixed point (focus) and a fixed line (directrix)
2. Derive the equation of a parabola with vertex at the origin, focus at (0, p), and directrix y = -p, obtaining y = x^2/(4p)
3. Identify the focus, directrix, and vertex of a parabola from its equation in standard form
4. Write the equation of a parabola given its focus and directrix for both vertical and horizontal orientations
5. Connect the geometric definition of a parabola to the vertex form of a quadratic function y = a(x - h)^2 + k

Prerequisites

• Derive circle equation