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Asymptotes of Hyperbola

Definition Asymptotes are tangents to the curve at infinity.
For hyperbola 75412.png, equation of pair of asymptotes is 75406.png.
Thus equation of hyperbola and that of its pair of asymptotes differ by constant k only.
Slopes of asymptotes are ± 75394.png.
Angle between asymptotes is θ = tan–175388.png.
For rectangular hyperbola, asymptotes are x – y = 0 and x + y = 0 which are perpendicular.
Axes of hyperbola are bisectors of pair of asymptotes.

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