9.1. General Form of a Conic http://www.ck12.org
9.1 General Form of a Conic
Here you will see how each conic section is the intersection of a plane and a cone, review completing the square and
start working with the general equation of a conic.
Conics are a family of graphs that include parabolas, circles, ellipses and hyperbolas. All of these graphs come from
the same general equation and by looking and manipulating a specific equation you can learn to tell which conic it
is and how it can be graphed.
What is the one essential skill that enables you to manipulate the equation of a conic in order to sketch its graph?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61843http://www.youtube.com/watch?v=iJOcn9C9y4w James Sousa: Introduction to Conic Sections
Guidance
The word conic comes from the word cone which is where the shapes of parabolas, circles, ellipses and hyperbolas
originate. Consider two cones that open up in opposite directions and a plane that intersects it horizontally. A flat
intersection would produce a perfect circle.
To produce an ellipse, tilt the plane so that the circle becomes elongated and oval shaped. Notice that the angle that
the plane is tilted is still less steep than the slope of the side of the cone.