## Conic Sections

Circle & Ellipse:

A circle is a special ellipse in which the two foci coincide (i.e., same point). Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone.

In an

*x*-

*y*coordinate system, the circle with center (h, k) and radius

*r*is the set of all points (

*x*,

*y*) such that

(x − h)

^{2}+ (y − k)^{2}= r^{2}Parabola:

The parabola is a conic section generated by the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface.

The hyperbola is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone.