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 = r2
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.
