Explanation

A hyperbola is the set of points where the difference of distances from two fixed points (foci) is constant.

Standard forms:

1. Horizontal: (x − h)² / a² − (y − k)² / b² = 1

2. Vertical: (y − k)² / a² − (x − h)² / b² = 1

Key points:

• Center: (h, k)

• Opens left/right or up/down depending on the form

• Asymptotes help guide the shape

Example:
(x² / 9) − (y² / 16) = 1 → center (0,0), opens left/right