A cone is a 3 dimensional object. It is obtained when one of the pair of intersecting lines is rotated about the other line in such a way that the angle between the lines is constant.
The point of intersection of lines is known as the vertex of cone, the fixed line is known as the axis and the rotating line is known as the generator of the cone. We get 2 equal portions, which are known as nappes.
When a plane intersects a cone, we get a conic section. It depends on the inclination of the plane w.r.t. the axis.
If the plane is perpendicular to the axis, we get a circle.
If the plane is NOT parallel to the generator, passes through only 1 nappe and does not contain the vertex, we get an ellipse.
If the plane is parallel to the generator and does not contain the vertex, we get a parabola.
If the plane is NOT parallel to the generator, passes through both nappes and does not contain the vertex, we get a hyperbola.
If the plane passes through the vertex of cone and contains the axis, we get a pair of straight lines.