Conic Sections
 Conic sections
Conic sections or conics are the curves that are obtained by intersecting a plane with a doublenapped right circular cone. Circles, ellipses, parabolas and hyperbolas are examples of conic sections.
A doublenapped 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 doublenapped cone:
If θ_{1}is the angle between the axis and the generator and θ_{2}is the angle between the plane and the axis, then, for different conditions of θ_{1}and θ_{2}, we get different conics, which are described with the help of a table as shown below.
Condition 
Conic Formed 
Figure 
θ_{2} = 90° (Only one nappe of the cone is entirely cut by the plane) 
A circle 

θ_{1}< θ_{2}< 90° (Only one nappe of the cone is entirely cut by the plane) 
An ellipse 

θ_{1} = θ_{2} (Only one nappe of the cone is entirely cut by theā¦ 
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