Formation of Circle, Ellipse, Parabola and Hyperbola from Cone
A parabola is the locus of points that is equidistant from both a certain point (called the focus) and a certain line (called the directrix). The parabola is the conic section that is obtained by slicing the cone parallel to the edge of the cone.
Fig: Creating a Parabola
The section is an ellipse when a plane is inclined to the axis and cuts all the generators.( a generator is a straight line which runs from the apex of the cone to the base )
The section is a parabola when the plane is parallel to a generator, and only one of the cone.
The section gives a hyperbola when the cutting plane is inclined at an angle greater than the exterior angle of the cone.