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