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Math Assignment Help With Forms of Hyperbola

7.6.3 Forms of Hyperbola:

  1. i) Rectangular Hyperbola: A hyperbola having equal axes is said to be rectangular hyperbola. i.e.

2b = 2a or b = a

In this case the equation of hyperbola is given as;

x2 – y2 = a2

  • ii) Vertical form of Hyperbola:

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The foci are taken at F(0,c) and F’ (0, -c), the equation of the hyperbola is of the form;

x2 ‗ y2 = 1, where b = √(c2 – a2)

a2 b2

The equation of the vertical form of hyperbola is

xi2 – yi2 = a2

Points to remember:

  • i) Foci F(ae, 0) & F’(-ae, 0)
  • ii) Centre O(0,0)
  • iii) Length of transverse axis = 2a
  • iv) Length of conjugate axis = 2b
  • v) Equations of directrices = x = ± (a/e)
  • vi) Vertices are A(a,0) & A’ (-a,0)
  • vii) Eccentricity = e = √(a2 + b2)/a

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