PPT-10.5 CONIC SECTIONS

Spring 2010 Math 2644 Ayona Chatterjee Conic sections result from intersection a cone with a plane PARABOLAS A parabolas is the set of points in a plane that are equidistant from a fixed point F called the focus and a fixed line called the directrix. area. and . the . origin. of . the . name. parabola. Kristjana. . Qosia. , Maria . Ntrinia. , Christina . Ioannou-Pappa. 8. th. . Lyceum of Athens. The discovery of conic sections is ascribed to Menaechmus. He tried to solve the problem of the duplication of cube using Hippocrates’ discovery that this problem can be reduced to the problem of finding two mean proportional in continued proportion between two given straight lines. Actually construction of a segment x such that x. We know that the standard equations of the ellipse are as follows: , where (horizontal major axis)or , where (vertical major axis)In order to find the information asked for, we must convert to st Graphing these two points in a coordinate system allows us to recognize that this must be an ellipse with a horizontal major axis since the foci always lie on the major axis. , where NOTE: Graphing Conic sections will be defined in two different ways in this unit.. The set of points formed by the intersection of a plane and a double-napped cone.. The set of points satisfying certain conditions in relationship to a fixed point and a fixed line or to two fixed points. Find the equation of the conic section using the given information. Ellipse: co-vertices . and foci .  . Find the equation of the conic section using the given . information.. Circle: center (-4,5) and tangent to the y-axis. Basic hyperbola vocab. Hyperbola. : Set of all points P such that the . difference. of the distance between P and two fixed points (foci) is a constant. Vertices. : The line through the foci intersects the hyperbola at the vertices. Module 10. HigherEdServices.org. Session topics. Cutting planes. Cross Sections. Multiple Cross Sections. Cutting Planes. A cutting plane is an imaginary plane that slices through an object. Cutting Plane. ROMAN V KOCHANOV. , IOULI E GORDON, LAURENCE S. ROTHMAN, Atomic and Molecular Physics, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA; KEITH SHINE, Department of Chemistry, University of Reading, Reading, United Kingdom; STEVEN W. SHARPE, TIMOTHY J. JOHNSON, Chemical Physics and Analysis, Pacific Northwest National Laboratory, Richland, WA, USA; JEREMY J. HARRISON, Department of Physics and Astronomy, University of Leicester, Leicester, United Kingdom; PETER F. BERNATH, Department of Chemistry and Biochemistry, Old Dominion University, Norfolk, VA, USA; TIMOTHY WALLINGTON, Research and Advanced Engineering, Ford Motor Company, Dearborn, MI, USA; MANFRED BIRK, GEORG WAGNER, Remote Sensing Technology Institute, DLR, . Parabola: the collection of all points that are equidistant from a point(focus) and a line(. directrix. ). 1. Distance from A to focus:. Distance from B to focus:. Distance from C to focus:. 2. Vertex at. Dr. Shildneck. Fall, 2014. The Ellipse. An ellipse is a locus of points such that the sum of the distances between two fixed points (called the foci) is always the same.. The axis that runs through the longer part of the ellipse is called the major axis. The points at the ends of the major axis are called the vertices.. Section 11.6 – Conic Sections. Parabola – set of points in a plane that are equidistant from a fixed point (. d(F, P). ) and a fixed line (. d (P, Q). ).. Focus - the fixed point of a parabola.. Directrix - the fixed line of a parabola.. TThheessiimmpplleeaannddccoonnvveenniieenncceepprreevveennttssccrraattcchheesssshheeeettNEWSDec 2014TEL81-868-38-6154 FAX81-868-38-6331E-mail toolsconiccojpURL http//wwwconiccojp/EnPage/indexhtmlEEaas Sections of a right cone. The Conics in everyday life. Terminology. Conics . as plane . loci - Problems. Double Hyperbola. Conics as plane loci. Four Conic Sections. Conics in a rectangle. More Problems. July 28029,2016 Berlin, Germany. Exact analytical aberration theory . of centered optical systems . containing conic surfaces. Boian. . Andonov. . Hristov. , Prof. (. Ph.D. ) . Bulgarian Academy . of Sciences.