Teacher Resources for Instructional Planning


Precalculus Std 3: Graph conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations. Example: graphing x² – 6x + y² – 12y + 41 = 0 or y² – 4x + 2y + 5 = 0 Formulating equations of conic sections from their determining characteristics Example: writing the equation of an ellipse with center (5, -3), horizontal major axis of length 10, and minor axis of length 4

Lesson Plans Conic Lessons This is an online lesson that is easily transferable to lecture notes. It reads like a textbook with lots of examples and explanations. It starts with circle and moves through hyperbola, including intersections of conics and conics with linear graphs. The Blue Room in the White House This is very creative look at the Blue Room in the White House (Elliptically shaped). The lesson refers to the white house site and encourages students to graph the floor plan and find the equation of the ellipse. Chicago Public Schools This lesson for day 125 provides exhaustive discussion of general form for conic section with printable rules for determining nature of a conic from equation.. Solving Systems of Second Degree Equations This site provides considerable background on second degree equations with examples. An online quiz is available. Conics by Inspection Exhaustive discussion of the general equation with an emphasis on the degenerate cases. Calculator Conics This site is a detailed explanation of conic sections that guides students through the use of the TI-83 calculator to graph conic sections in Function mode. There is a mention of degenerate and rotated conics.

Resources: Conic Section Details This is an advanced, but interesting link on conic sections at Wolfram research. Interactive Slice of a Cone VRML view of a plane intersecting a cone. (Requires VRML program such as Cortona from parallel graphics. Download it here for free.) Conics in the News CNN article about how police track cell phone signals using the intersections of circles. Free PowerPoint Lessons Free PowerPoint lesson on conic sections including geometric and algebraic definitions. Go to chapter 12 and download the zip file. Degenerate Conic Sections from the Standard Form Notes about degenerate (rotated) conic sections nested within a large section on conics. Japanese Conic Applet This java applet demonstrates how the intersections of concentric circles form hyperbola. The applet allows students to rotate the foci about the origin. An explanation of degenerate conics follows. Conic Section Reference This site includes a reference table for conics that could serve as a reference during a test on conic sections. It includes the use of the discriminant with the standard form of a conic and degenerate conic sections.
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