Hyperbola of Class 11
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 = 1, asymptotes are y = ± b/a x. For = -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
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.