A hyperbola is defined as the locus of a point that moves in a plane such that its distance from a fixed point is always *e* times (*e* > 1) its distance from a fixed line. The fixed point is called the focus of the hyperbola. The fixed straight line is called the directrix and the constant *e* is called the eccentricity of the hyperbola.

Let *S* be the focus and the line *l* be the directrix. Draw *SX* perpendicular to the directrix. Divide *SX* internally and externally in the ratio *e* : 1 (*e* > 1). Let *A* and *A*′ be the point of division. Since and the points *A* and *A′* lie on the curve.

Let *AA*′ = 2

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