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Hyperbolas

Center (h, k)

A hyperbola centered at (h, k) will have the following standard equations:

  • If the transverse axis is horizontal, then

HyperbolasCenter1-1

Vertices: (h+a, k), (h-a, k)

Foci: (h+c, k), (h-c, k), where c2 = a2 + b2

Equations of asymptote lines: HyperbolasCenter1-2

  • If the transverse axis is vertical, then

HyperbolasCenter2-3

Vertices: (h, k+a) and (h, k-a)

Foci: (h, k+c) and (h, k-c), where c2 = a2 + b2

Equations of asymptote lines: HyperbolasCenter1-4