« Ellipse 

1. A hyperbola is the locus of points where the difference in the distance to two fixed points (called the foci) is constant.
2. A hyperbola is the set of all points (x, y) in the plane the difference of whose distances from two fixed points is some constant. The two fixed points are called the foci.
A hyperbola comprises two disconnected curves called its arms or branches which separate the foci.
Hyperbola can have a vertical or horizontal orientation.
Standard equation of a hyperbola centered at the origin (horizontal orientation)
Example 1:
Standard equation of a hyperbola centered at the origin (vertical orientation)
Example 2:
The foci for a horizontal oriented hyperbola are given by
The foci for a vertical oriented hyperbola are given by
Asymptotes of a horizontal oriented hyperbola are determined by
Asymptotes of a vertically oriented hyperbola are determined by
The eccentricity is given by
Example 3:
Consider the equation
Find: a, b, foci, asymptotes, and eccentricity.
Foci:
Asymptotes:
Eccentricity:
Picture:
Horizontal oriented hyperbola centered at (u, v)
Vertical oriented hyperbola centered at (u, v)
Foci:
The foci for a horizontal oriented hyperbola centered at (u, v):
The foci for a vertical oriented hyperbola centered at (u, v):
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Asymptote:
Asymptotes of a horizontal oriented hyperbola are determined by
Asymptotes of a vertically oriented hyperbola are determined by
Eccentricity:
The eccentricity is given by
Horizontal oriented hyperbola:
Vertical oriented hyperbola: