PPT-Hyperbola

By Leonardo Ramirez Pre Calculus Per6 Mr Caballero Hyperbola What is a Hyperbola The term hyperbola was introduced by the Greek mathematician Apollonius of Perga as well as the terms Parabola and Ellipse . Hyperbola - - Center at (h, k ) Equation Asymptotes Center (h, k) (h, k) Ver tices (h + a, k); (h - a, k) (h, k + a); (h, k - a) Foci (h + c, k) ; (h - c, k) (h, k + c); Traces in (Hyperbola class): Traces in (Hyperbola class): Traces in (Ellipse / Circle class): PARTS OF A HYPERBOLA. center. Focus 2. Focus 1. conjugate axis. vertices. vertices. The dashed . lines are asymptotes for the . graphs. transverse axis. A . hyperbola. is the collection of . points . Hyperbola: a set of all points (x, y) the difference of whose distances from two distinct fixed points (. foci. ) is a positive constant. . Similar to ellipse, which is the SUM of distances. Every hyperbola has two disconnected branches. The line through the foci intersects a hyperbola at its two . Date: ______________. Horizontal. transverse axis:. 9.5 Hyperbolas. x. . 2. a. 2. y. 2. b. 2. –. = 1. y. x. V. 1. (–. a. , 0). V. 2. (. a. , 0). Hyperbolas with Center (0,0). asymptotes: . y. = ± . Definitions. . A. . hyperbola. . is the set of all point P such that the difference of the distances between P and two fixed points, called the . foci. , is a constant. . The. . transverse axis. . 12:Section6. Quadric Surfaces. Written by Richard Gill. Associate Professor of Mathematics. Tidewater Community College, Norfolk Campus, Norfolk, VA. With Assistance from a VCCS Learning Ware Grant. x. Graph hyperbolas by using the foci of a hyperbola. Hyperbolas. Result from slicing both cones in a double cone with one plane. Have 2 foci which determine the shape . Each branch opens away from the center.. Coordinate Systems. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Last modified: . 29. th. August 2015. Conic Sections. In FP1 and FP3, we’ll be examining different types of curves.. All the ones you’ll see can be obtained by taking ‘slices’ of a cone (known as a . 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.. difference. of the distances from two fixed points is a constant.. Section 7.4 – The Hyperbola. Section 7.4 – The Hyperbola. Q.  .  .  . Hyperbola – a set of points in a plane whose . difference. GeoGebra. Ann . Schnurbusch. Southeast Missouri State University. Occurrence of the Conics. http://britton.disted.camosun.bc.ca/jbconics.htm. (All general info about conics is from this website.). Mathematicians have a habit of studying, just for the fun of it, things that seem utterly useless; then centuries later their studies turn out to have enormous scientific value.  There is no better example of this than the work done by the ancient Greeks on the curves known as the conics: the ellipse, the parabola, and the hyperbola. They were first studied by one of Plato's pupils. No important scientific applications were found for them until the 17th century, when . ii Pacific Northwest Coast (PN)Variant OverviewForest Vegetation SimulatorCompiled By:Chad E. KeyserUSDA Forest ServiceForest Management Service Center2150 Centre Ave., Bldg A, Ste 341aFort Collins 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.