Mathematics
Conics
Parabola

Parabola

A parabola is defined as:

dist (P,F) = dist(P,L)

P is any point on the curve. F is the focus of the parabola, L is the directrix; and "dist" is the distance between the two related points.

Let's express the above equation:
sqrt [(c - x)² + (0 - y)² ] = [(- c - x)² + (y - y)²]^1/2

[(c - x)² + y² ]^1/2 = [(c + x)² ]^1/2

[c² - 2cx + x² + y²]^1/2 = [c² + 2cx + x² ]^1/2

c² - 2cx + x² + y² = c² + 2cx + x²

Then: y² = 4cx

y² = 4cx

That is the equation of a parabola.