Various Measures of Hyperbola

Foci,Vertices, Transverse and Conjugate Axes, Directrices and Centre of the Hyperbola x²/a² - y²/b² = 1

Foci: The points S(ae,0) and S’ (-ae,0) are the foci of the hyperbola.

Vertices: Where curve meets the line joining the foci S and S’, are called the vertices of the hyperbola (A,A’).

Transverse Axis: The straight line joining the vertices A and A’ is called the transverse axis of the hyperbola. Its length is taken to be 2a.

Centre of the hyperbola:

The middle point of AA’ is called the centre of the hyperbola. It bisects every chord of the hyperbola that passes through it.

Conjugate axis:

The straight line through the centre which is perpendicular to the transverse axis does not meet the hyperbola in real points.

But if B, B’ are points on this line such that CB = CB’ = b, the line BB’ is called the conjugate axis such that BB’ = 2b.