Parabola

Explanation

A parabola is the set of points equidistant from a fixed point (focus) and a fixed line (directrix).

Standard forms:

1. Vertical: (x − h)² = 4p(y − k)

2. Horizontal: (y − k)² = 4p(x − h)

Where:

• (h, k) = vertex

• p = distance from vertex to focus

Key points:

• Opens up/down if vertical

• Opens left/right if horizontal

Example:
y² = 8x → vertex (0,0), opens right, p = 2