Other Form of Hyperbola

There is another standard hyperbola in which the transverse axis is along y-axis. If the transverse axis is along y-axis and the conjugate axis is along x-axis, then the equation of the hyperbola is

For this type of hyperbola,

Centre: C(0, 0)

Vertices: A(0, a), A′(0, −a)

Foci: F1(0, ae), F2(0, −ae)

Equation of transverse axis is x = 0

Equation of conjugate axis is y = 0

End points of conjugate axis: (b, 0), (−b, 0)

Equations of latus rectum: y = ±ae

Equations of directrices: y= ±a/e

End points of latus rectum: (±b2/a, ae), (±b2/a, −ae)