Asymptotes
Hyperbola of Class 11
Asymptotes
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The straight line which tends to be a tangent to a curve as the point of contact approach infinity, is called an asymptote of the curve. In other words, an asymptote tends to touch the curve at infinity.
For Angle between asymptotes = 2tan-1(b/a) If angle between asymptotes is 90°, i.e. 2tan-1(b/a) = 90° or b/a = 1 ⇒ b = a |
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= 1, asymptotes are y = ± b/a x. For 
So hyperbola becomes x2 − y2 = a2 and is called rectangular hyperbola.
In general the equation of the hyperbola and its pair of asymptotes differ by a constant. For example if S = 0 is the equation of the hyperbola, then the equation of the asymptotes is given by S + λ = 0. The constant λ is determined by using the condition that S + λ = 0 represents a pair of straight lines.
