Hyperbole – Conic Section – Educational Animations

Hyperbole – conic section – educational animations


In mathematics, especially in geometry, hyperbole is a conic curve, this means that it is formed with the points that simultaneously belong to a cone and to a plane that cut it off.

Below, you will see animations of various properties of the hyperbole, especially those that  differenciate it from the conic curves parábola e elipse.


Hyperbole – conic section


When a straight circular cone is sectioned by an oblique plane to the axis of the cone and forming with this axis an angle smaller than the angle that the generatrix forms with the axis, and may even be parallel to it, the points that belong to both the plane and the Cone forms a hyperbole.



The module of the difference of distances from any point of the hyperbola to two fixed points (called foci) is always equal to the distance between the vertices of the hyperbola.


FOCUS: They are the two fixed points of hyperbole.

VERTICES: These are the points that hyperbole has in common with the axis.

CROSS SHAFT: It is the axis cut by hyperbole.

NON-CROSS SHAFT: It is the axis that is not cut by hyperbole.

ASSIGNMENTS: Straight lines in which the branches of hyperbola are tangent in infinity.


If the plane contains the VERTIX of the cone and is parallel to its axis we will not have a hyperbole but straight lines.

Eduardo Stefanelli

Engenheiro por profissão, professor por vocação