Conic sections

While creating a resource page, please click here for a resource creation checklist.

Concept Map 

flash

= Textbook = To add textbook links, please follow these instructions to: ([ Click to create the subpage])

=Additional Information=

Reference Books
= Teaching Outlines = This page describes the various two dimensional conic sections that can be obtained.

Learning objectives

 * 1) Conic Sections are figures that can be formed by slicing a three dimensional right circular cone with a plane.
 * 2) There are different ways to do this, and each way yields a different figure.
 * 3) These figures can be represented on the graph as well as algebraically.
 * 4) The four conic sections are circles, ellipses, parabolas, and hyperbolas.

Notes for teachers

 * 1) The general equation for all conics is $$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$$
 * 2) If $$B^2-4AC<0$$ then the curve is an ellipse, circle, point or no curve.
 * 3) If $$B^2-4AC=0$$ then the curve is a parabola,2parallel lines, 1 line or no curve.
 * 4) If $$B^2-4AC>0$$ then the curve is a hyperbola or 2 intersecting lines.

Activity No #

 * Estimated Time: 40 minutes
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Learning objectives

 * 1) Introduction to the form of a hyperbola

Activity No #
<ggb_applet width="1440" height="673" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false" />
 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets


 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner


 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Learning objectives

 * 1) Introduction to the form of a hyperbola

Notes for teachers

 * Activity No #
 * Click to Comment


 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner


 * Activity No #
 * Click to Comment


 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

= Hints for difficult problems =

= Project Ideas =

= Math Fun =

Usage

Create a new page and type to use this template