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Asymptotes of a Hyperbola
The asymptotes of a hyperbola are intersecting straight lines that the branches of the graph approach as the values of and get larger and larger, but never actually intersect. For a hyperbola centered at the origin, , the asymptotes correspond to the extended diagonals of a central rectangle. When the transverse axis is on the -axis, the rectangle's sides intersect at the vertices and at , giving the asymptote equations and . When the transverse axis is on the -axis, the rectangle's sides intersect at the vertices and at , giving the asymptote equations and .
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Intermediate Algebra @ OpenStax
Ch.11 Conics - Intermediate Algebra @ OpenStax
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