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Hyperbola Properties
Hyperbola Properties
Foci, vertices, and asymptotes of a hyperbola
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Orientation
Horizontal (opens left/right)
Vertical (opens up/down)
Semi-transverse axis (a)
Semi-conjugate axis (b)
Center x (h)
Center y (k)
(x − 0)² / 3² − (y − 0)² / 4² = 1
Center
(0, 0)
Focal distance (c)
5
Eccentricity (e)
1.666667
Latus rectum (2b²/a)
10.6667
Vertices
(-3, 0), (3, 0)
Co-vertices
(0, -4), (0, 4)
Foci
(-5, 0), (5, 0)
Asymptotes
y = 1.3333·(x − 0) + 0
y = −1.3333·(x − 0) + 0
Directrices
x = 0 + 1.8
x = 0 − 1.8
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Hyperbola Properties
Plot of the hyperbola: its two branches, center, vertices, foci, and dashed asymptotes through the center.
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