PPT-HYPERBOLA

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 . Traces in (Hyperbola class): Traces in (Hyperbola class): Traces in (Ellipse / Circle class): 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. = ± . By: Leonardo Ramirez. Pre Calculus. Per.6. 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. . 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. 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. 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 . The Ellipse. Basic oval. Has a center point, 2 foci, focal axis, and 2 vertices on the focal axis. https://. www.youtube.com/watch?v=7UD8hOs-vaI. The ellipse. The ellipse: formulas. Ellipses with center (0, 0). Parabolas are shaped like a U or C. Parabolas. Equations -. y-k . = a(x - h). 2. . opens up if a > 0, opens down if a < 0.. x-h. . = a(y - k). 2. . opens right if a > 0, opens left if a < 0..