Conic Sections
Circles , ellipses , parabolas and hyperbolas are known as conic sections because they can be obtained as intersections of a plane with a double napped right circular cone .
These curves have a very wide range of applications in fields such as planetary motion , design of telescopes and antennas , reflectors in flashlights and automobile headlights , Projectile motion , sand clock , Ball etc
Double-napped right circular cone : Let l be a fixed vertical line and m be another line intersecting it at a fixed point V and inclined to it at an angle α . Suppose we rotate the line m around the line l in such a way that the angle α remains constant . Then the surface generated is a doublenapped right circular hollow cone herein after referred as double-napped right circular cone .
If we take intersection of a plane with a cone , section so obtained is called a conic section . We obtain different kinds of conic sections depending on the position of the intersecting plane with respect to the cone and by the angle made by it with the vertical axis of the cone .