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:

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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