Asymptotes

Hyperbola of Class 11

Asymptotes

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 Equation of tangent = 1, asymptotes are y = ± b/a x. For Equation of tangent = -1, we have same asymptotes.

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

Asymptotes

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.

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