Pre-Calculus: Illustrating Conic Sections PDF
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These notes explain conic sections, including parabolas, ellipses, circles, and hyperbolas and how they relate to shapes found in architecture, such as St. Paul's cathedral. The document includes diagrams and examples.
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Illustrating Conic Sections At the end of the lesson, you will be able to: ✓ illustrate the different types of conic sections: parabola, ellipse, circle, hyperbola, and degenerate cases; and ✓ give real-life examples of objects and concepts where these conic sections are applied. Conic S...
Illustrating Conic Sections At the end of the lesson, you will be able to: ✓ illustrate the different types of conic sections: parabola, ellipse, circle, hyperbola, and degenerate cases; and ✓ give real-life examples of objects and concepts where these conic sections are applied. Conic Section In mathematics, a conic section (conic) is a curved obtained by the intersection of the surface of a cone with a plane. axis vertex generator vertex vertex angle nappe directrix Formation of Conic Sections Ways on how the double right circular cone is cut by a plane The angle between the plane and the axis is greater than the vertex angle ELLIPSE Formation of Conic Sections Ways on how the double right circular cone is cut by a plane The plane is perpendicular to the axis CIRCLE Formation of Conic Sections Ways on how the double right circular cone is cut by a plane The angle between the plane and the axis is equal to the vertex angle PARABOLA Formation of Conic Sections Ways on how the double right circular cone is cut by a plane The angle between the plane and the axis is less than the vertex angle HYPERBOLA Degenerate Conics POINT LINE TWO LINES Performance Task Look for a man-made construction or structure that incorporates the form or pattern of a conic section. Include a detailed caption explaining the conic section used and its significance in the structure. Print or paste it in a short bond paper. Performance Task Rubrics Example St. Paul's Cathedral boasts a fascinating architectural marvel: the Whispering Gallery. This circular chamber is actually an elliptical shape, a property that creates an extraordinary acoustic phenomenon. A whisper emitted at one focus of the ellipse can be clearly heard at the other focus, yet remains inaudible at any other point in the room. This intriguing application of geometric principles adds a touch of magic to the cathedral's grandeur.
