PPT-Lecture 31 – Conic Sections

Parabola the collection of all points that are equidistant from a pointfocus and a line directrix 1 Distance from A to focus Distance from B to focus Distance from C to focus 2 Vertex at. 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. 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 Eccentricity – . The ratio of distances. . It basically tells how close a conic section is to being a circle.. In a parabola: . . e. . = 1. In an ellipse or hyperbola:. The . ratio between the foci and the vertices. Michael Woltermann. Mathematics Department. Washington and Jefferson College. Washington, PA 15301-4801. Triumph der Mathematik. 100 Great Problems of Elementary Mathematics. By Heinrich D. Written by Gaurav Rao. Last edited: 10/3/15. What Are Conics?. Conics are cross sections of a cone. Locus of points that distance from a point (focus) . And a line (. directrix. ) are at a fixed ratio(eccentricity). OTHER VIEW OF CONIC SECTIONS. THE CIRCLE. CONIC SECTION – THE CIRCLE. Equation for a Circle. Standard Form: x² + y² = r². You can determine the equation for a circle by using the distance formula then applying the standard form equation.. 11.1 - An . Introduction. Conic Sections - Introduction. A conic is a shape generated by intersecting two lines at a point . (vertex) and . rotating one line . (generator) around . the other . (axis) while . What are Cross Sections?. Cross Sections are defined as the shape we get when cutting straight through an object. They can be determined by how the cross section flows…whether vertically or horizontally.. , . PARABOLA. AND . HYPERBOLA. ARE CALLED CONIC SECTIONS. BECAUSE . THESE CURVES APPEAR ON THE SURFACE OF A CONE . WHEN IT IS CUT BY SOME TYPICAL CUTTING PLANES.. Section Plane. Through Generators. 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.. © 2010 Pearson Education, Inc. . All rights reserved. Chapter 9. Analytic Geometry. © 2010 Pearson Education, Inc. All rights reserved. 2. Conic Sections: Overview. Most of the sections in this chapter focus on the plane curves called . 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. Parametric Equations. 6. .1 . Introduction. The General Quadratic Equation in x and y has the form:. Where A, B, C, D, E, F are . constants.. The graphs of these equations are called . Conic Sections.