PPT-CONIC SECTIONS 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. Example 2: Find the coordinates of the center, vertices, foci, and the equations of the asymptotes of the hyperbola given by . We know that the standard equations of the hyperbola are as follows: , 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 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. 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).. 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. 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 . , . 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. Algebra 2. Chapter 9. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. Robert Davidson and Bob Gardner Department of Mathematics and Statistics East Tennessee State University. Online at: . http://www.etsu.edu/math/gardner/stooges/Stooges-Trig-2012.ppt. Other Features HEC-RAS Jon Fripp NDCSMC 2016 Module 8: Other Features Horizontal variation in Manning’s n Vertical variation in Manning’s n Floodway encroachments Graphical cross section editing TThheessiimmpplleeaannddccoonnvveenniieenncceepprreevveennttssccrraattcchheesssshheeeettNEWSDec 2014TEL81-868-38-6154 FAX81-868-38-6331E-mail toolsconiccojpURL http//wwwconiccojp/EnPage/indexhtmlEEaas 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.