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in JEE by kratos

Defind Hyperbola as a set of points and derive the equation of hyperbola in standard form x2/a2 - y2/b2 = 1

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+2 votes
by kratos
 
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Definition hyperbola: A Hyperbola is the act of all points in a plane the difference of whose distances.

From two fixed points in the plane is constant.

The two fixed points are called Focii and the mid point ‘O’ is called the centre of the hyperbola.

Distance between two focii F1 and F2 = 2c

Distance between two velocities = AB = 2a

(length of transverse axis) and b = √(c2 - a2)

∴ 2b = length of conjugate axis and e = c/a is called the eccentricity of the hyperbola.

Derivation : Equation of hypergola in standard form x2/a2 - y2/b2 = 1

Squaring on both side

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