Conic sections
Let l be a fixed vertical line ( tick 1 and a)and m ( tick 2 and b ) be another line intersecting it at a fixed point V and inclined to it at an angle α ( tic 3 and c ).Suppose we rotate the line m around the line l in such a way
that the angle α remains constant.( play animation) Then the surface generated is a double-napped right circular hollow cone herein after referred as cone and extending indefinitely far in both directions The point V is called the vertex; the line l is the axis of the cone. The rotating line m is called a generator of the cone. The vertex separates the cone into two parts called nappes. If we take the intersection of a plane with a cone, the section so obtained is called a conic section. ( tick Conics) Thus, conic sections are the curves obtained by intersecting a right circular cone by a plane.