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A hyperbola is the locus of a point which moves such that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line.
Fixed point is called focus, fixed straight line is called directrix and the constant ratio is called eccentricity of the Hyperbola. Eccentricity is denoted by e and e > 1. PS/PM = e
Alternate Definition It is the locus of a point which moves such that difference of its distances from two fixed points remains constant.
|PS′ − PS| = 2a