Let L₁ be fixed vertical line and L₂ be another line, intersecting the line L₁ at a fixed point 'V' and inclined to it an angle 'α'.

Suppose we rotate the line L₂ around the line L₁ in such a way the angle remains constant, then form a double right circular cone.

The point 'V' is called the vertex, the line L₁ is the axis of cone. The rotating line L₂ is called generator of a cone.

• Perimeter of base is called directrix.
• Lateral surface of right circular cone is called nappe.
• Here two nappes are there, vertex above one is called upper nappe and vertex below one is called lower nappe.
• The angle between axis and generator is called semi-vertical angle (α) of cone.
• If plane intersecting the double right circular cone, we get two dimensional curves, these curves are called conic sections.
• Depending on angle made by the plane with the vertical axis of cone, the plane cuts the cone into three different ways.
• Let the angle between plane and axis of cone is 'β'.

Generated conics:

Suppose the cutting plane makes an angle 'β' with axis of cone and suppose the semi vertical angle of cone is α.

Then conic section is

• an Ellipse; if α < β < π/2 (0 < e < 1)
• a circle; if β = π/2 (e = 0)
• a parabola; if α = β (e = 1)
• a hyperbola; if 0 ≤ β < α (e> 1)

Where e =

i.e, generated conics are ellipse, circle, parabola and hyperbola.

Degenerated conics

If a plane intersect the double right circular cone at its vertex, then formed figures are called degenerated conics.

In this case

• Ellipse becomes a point
• Parabola becomes a line
• Hyperbola becomes a pair of intersecting lines