Conic Sections Presentation PDF
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This presentation covers conic sections, including circles, parabolas, ellipses, and hyperbolas. It explains the shapes created by the intersection of a plane and a double right circular cone, with illustrative examples and definitions. The presentation also includes examples like hills, wheels, and orbits to demonstrate how conic sections appear in various real-world scenarios.
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PRE-CALCUL US Pre-Calculus: CONIC SECTIONS Learning Objectives: 1.Define Conics 2.Illustrate the different conic sections; 3.Distinguish the different conic sections; and 4.Show appreciation to the concept CONIC SECTIONS A conic section, or simpl...
PRE-CALCUL US Pre-Calculus: CONIC SECTIONS Learning Objectives: 1.Define Conics 2.Illustrate the different conic sections; 3.Distinguish the different conic sections; and 4.Show appreciation to the concept CONIC SECTIONS A conic section, or simply conic, is a curve formed by the intersection of a plane and a double right circular cone. CONIC SECTIONS A conic section, or simply conic, is a curve formed by the intersection of a plane and a double right circular cone. TYPES OF CONIC SECTIONS 1 Circl e 3 Parabol a Ellipse Hyperbol 2 4 a TYPES OF CONIC SECTIONS Circle - the cutting plane is not parallel to any generator but is perpendicular to the axis TYPES OF CONIC SECTIONS Ellipse - the cutting plane is not parallel to any generator TYPES OF CONIC SECTIONS Parabola - the cutting plane is parallel to one and only one generator TYPES OF CONIC SECTIONS Hyperbola- the cutting plane is parallel to the axis of the double cone - is perpendicular to the bases of the two cones TYPES OF CONIC SECTIONS Circle Ellipse Parabola Hyperbol a TYPES OF CONIC SECTIONS Circle Ellipse Parabola Hyperbol a DEGENERATE CASES: Poin t Line Intersecting lines DEGENERATE CASES: Point - the cutting plane passes through the vertex of the cone DEGENERATE CASES: Line - the cutting plane passes through the generators DEGENERATE CASES: Intersecting lines - the cutting plane passes through the axis DEGENERATE CASES: Point Line Intersectin g lines Example: Classify the following objects as to which type of conic they represent. Hill Answer: PARABOLA Example: Classify the following objects as to which type of conic they represent. Wheel Answer: CIRCLE Example: Classify the following objects as to which type of conic they represent. Imaginary Orbit Answer: ELLIPSE Example: Classify the following objects as to which type of conic they represent. Athletic Field Answer: ELLIPSE EXERCIS E:Identify the appropriate types of conic section that each picture represents 1. 2.3.4.5. 6 7 8 9 10..... Exercise: For 20 points Draw anything that shows the four conics. THANK YOU May GOD bless you always!
