Hyperbola:
A hyperbola is locus of a point which moves such that, the ratio of its distance from a fixed point (which is focus) and its distance from a fixed straight line (which is directrix), is a constant (which is eccentricity). This constant (which is eccentricity) is greater than unity.
Standard equation and basic definitions
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(i) The eccentricity e can be given by the relation 
(ii) As the curve is symmetrical about y - axis, it is clear that there exists another focus S' at (-ae, 0) and a corresponding directirx Z'M' with equation x= -a/e
(iii) The points A and A' are called as vertices of the hyperbola.
(iv) The straight line joining vertices is called as transverse axis of hyperbola, its length AA' is 2a.
(v) The straight line BB' is called as conjugate axis.
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Illustration: Find eccentricity of hyperbola which passes through (3, 0) and (3√2, 2).
Solution: Let the hyperbola be
∴ It passes through (3, 0) and (3√2, 2)
Which give a2 = 9 and b2 = 4
∴ from b2 = a2(e2 -1), we get 4 = 9(e2 -1)
or 
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