What are Conic Sections?
Conic sections are the curves that result from the intersection of a double right cone and a plane. There are four types of conic sections: circles, ellipses, hyperbolas, and parabolas.
The general form of a conic section is:
Ax^2 + Cy^2 +Dx +Ey + F = 0,
where A and C cannot both equal to zero.
If AC = 0, the conic section is a parabola.
If AC > 0, the conic section is an ellipse or circle,
If AC < 0, the conic section is a hyperbola.
For more on the general form of conics, refer to the following video:
http://www.youtube.com/watch?v=hIFOHezw5ik
The general form of a conic section is:
Ax^2 + Cy^2 +Dx +Ey + F = 0,
where A and C cannot both equal to zero.
If AC = 0, the conic section is a parabola.
If AC > 0, the conic section is an ellipse or circle,
If AC < 0, the conic section is a hyperbola.
For more on the general form of conics, refer to the following video:
http://www.youtube.com/watch?v=hIFOHezw5ik
What is an Ellipse?
An ellipse is the collection of all points in the same plane, the sum of whose distance from two fixed points, called the foci, is a constant.
For a visual, find a piece of string (this represents the constant) and two thumbtacks (representing the foci). Stick the foci on a piece of cardboard so that the distance between them is less than the length of the string. Now attach the ends of the string to the thumbtacks and, using the point of a pencil, pull the string taut. Now rotate the pencil around the two thumbtacks. The pencil traces out an ellipse.
Terms and Definitions:
Major Axis - the line containing the foci, the longer axis
Minor Axis - the line through the center and perpendicular to the major axis, the shorter line
Vertices - the endpoints of the major axis
Co-vertices - the endpoints of the minor axis
Foci - (singular: focus) two fixed points on the major axis
Major Axis - the line containing the foci, the longer axis
Minor Axis - the line through the center and perpendicular to the major axis, the shorter line
Vertices - the endpoints of the major axis
Co-vertices - the endpoints of the minor axis
Foci - (singular: focus) two fixed points on the major axis
For the updated powerpoint version, click here: /uploads/2/2/5/5/22554190/ellipses_presentation.pptx