Conic Sections: Circle and Parabola

• Conic sections 

Conic sections or conics are the curves that are obtained by intersecting a plane with a double-napped right circular cone. Circles, ellipses, parabolas and hyperbolas are examples of conic sections.

A double-napped cone can be obtained by rotating a line (let us say m) about a fixed vertical line (let us say l).

Here, the fixed line l is called the axis of the cone and m is called the generator of the cone. The intersection (V) of l and m is called the vertex of the cone.

Different conics formed by intersecting a plane and a double-napped cone:

If θ₁is the angle between the axis and the generator and θ₂is the angle between the plane and the axis, then, for different conditions of θ₁and θ₂, we get different con…