* Overview of Conic Relations *
Conic Sections can actually be derived from views of slicing a 3D cone.
There are four basic Conic Sections: Circle, Ellipse, Hyperbola, Parabola.
They are illustrated below as graphs with their centers at the orgin of a
Rectangular Coordinate System or Cartesian Coordinate System.
The standard form for the equations of these Conic Sections is below:
Ax2 + Cxy + By2 + Dx + Ey = F
Note: A, B, C, D, E, F are non-zero real numbers
Note: Each variable is of second degree indicating it crosses each axis twice
however, the equation and graph of a Parabola is different since it is H or V.
They are not functions as Linear, Quadratic, and Polynomial Functions are
since they do not pass the vertical line test. The Vertical Line Test can be
thought of drawing a Vertical Line over a graph or curve then the line touches
only once then it is a function. Obviously, Conics fail the vertical line test
therefore they are not functions but called relations or sets of points.
Circle Ellipse
These Conic relations are all located with their center at the orgin.
Hyperbola Parabola
Each Conic Section can be oriented with it’s center at the orgin or not at center, also,
it can be instead of oriented horizonally, as shown above, it can be oriented vertically.