# Conics

A conical surface is formed by the rotation of a line, **g**, (also called the generatrix or generator) around another line, **e**, the axis, which is fixed at the point **V**, the vertex or apex, which forms the angle **α**.

The nappes are the upper and lower portions of the conical surface which is divided by the appex.

A conic section is the area of intersection of a conical surface with a plane that does not pass through its apex. Depending on the relationship between the angle of a conical surface, **α**, and the inclination of the plane with respect to the axis, **β**, the conic sections will be elipses, circles, parabolas or hyberbolas.

## Ellipse

**α < β < 90º**

If the plane cuts all the generators (of one nappe only) and it is not perpendicular to the axis, the conic section is an ellipse.

## Circle

If **β = 90°**, that is to say, the plane is perpendicular to the axis, the conic section is a circle.

## Parabola

**α = β**

If the plane intersecting the conical surface is parallel to the generatrix, the conic section is a parabola.

## Hyperbola

**α > β**

If the plane intersects two nappes of the conical surface and the angle of the generatrix, **α**, is greater than the inclination of the plane with respect to the axis, **β**, the conic section is a hyperbola.