Conic Section

Conic sections are the curves which can be derived from taking slices of a "double-napped" cone. (A double-napped cone, in regular English, is two cones "nose to nose", with the one cone balanced perfectly on the other.)

If you think of the double-napped cones as being hollow, the curves we refer to as conic sections are what results when you section the cones at various angles.

There are some basic terms that you should know for this topic: 

Center: the point (h, k) at the center of a circle, an ellipse, or an hyperbola. 

Vertex: in the case of a parabola, the point (h, k) at the "end" of a parabola; in the case of an ellipse, an end of the major axis; in the case of an hyperbola, the turning point of a branch of an hyperbola. 

Focus: a point from which distances are measured in forming a conic; a point at which these distance-lines converge, or "focus". 

Directrix: a line from which distances are measured in forming a conic. 

Axis: a line perpendicular to the directrix passing through the vertex of a parabola. 

Major axis: a line segment perpendicular to the directrix of an ellipse and passing through the foci; the line segment terminates on the ellipse at either end; also called the "principal axis of symmetry"; the half of the major axis between the center and the vertex is the semi-major axis. 

Minor axis: a line segment perpendicular to and bisecting the major axis of an ellipse; the segment terminates on the ellipse at either end; the half of the minor axis between the center and the ellipse is the semi-minor axis. 

Each conic has a "typical" equation form, sometimes along the lines of the following:

parabola: Ax² + Dx + Ey = 0
circle: x² + y² + Dx + Ey + F = 0
ellipse: Ax² + Cy² + Dx + Ey + F = 0
hyperbola: Ax² – Cy² + Dx + Ey + F = 0