Precalculus: Mathematics for Calculus
7th Edition
ISBN: 9781305115309
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 11.2, Problem 72E
DISCUSS: Is It an Ellipse? A piece of paper is wrapped around a cylindrical bottle, and then a compass is used to draw a circle on the paper, as shown in the figure. When the paper is laid flat, is the shape drawn on the paper an ellipse? (You don’t need to prove your answer, but you might want to do the experiment and see what you get.)
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
(11.2) A carpenter wishes to construct an elliptical table top from a sheet ofplywood, 4 ft by 8 ft. He will trace out the ellipse using the “thumbtack andstring” method. What length of string should he use, and how far apart should thetacks be located, if the ellipse is to be the largest possible that can be cut out ofthe plywood sheet?
Directions: Be able to draw/illustrate the given problems and show pertinent solutions.
1. Ellipse (Navigation):
Problem: A ship is navigating along a route defined by an elliptical path. The ship's current position is known, along with the major and minor axes of the ellipse. Determine the closest point on the ellipse to the ship's current position.
2. Whispering Gallery: The figure below shows the
specifications for an elliptical ceiling in a hall designed to be a
whispering gallery. In an whispering gallery, a person standing at
one focus of the ellipse can whisper and be heard by another
person standing at the other focus, because all the sound waves
that reach the ceiling from one focus are reflected to the other
focus. If the hall below is 140 feet in length with 30 feet tal
ceiling at its highest point. How far from the end walls will the
foci point be?
大
Chapter 11 Solutions
Precalculus: Mathematics for Calculus
Ch. 11.1 - A parabola is the set of all points in the plane...Ch. 11.1 - The graph of the equation x2 = 4py is a parabola...Ch. 11.1 - The graph of the equation y2 = 4px is a parabola...Ch. 11.1 - Label the focus, directrix, and vertex on the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 6ECh. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 8ECh. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...
Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 12ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 50ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 54ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 59ECh. 11.1 - Families of Parabolas (a) Find equations for the...Ch. 11.1 - Parabolic Reflector A lamp with a parabolic...Ch. 11.1 - Satellite Dish A reflector for a satellite dish is...Ch. 11.1 - Suspension Bridge In a suspension bridge the shape...Ch. 11.1 - Reflecting Telescope The Hale telescope at the...Ch. 11.1 - Prob. 65ECh. 11.1 - Prob. 66ECh. 11.2 - An ellipse is the set of all points in the plane...Ch. 11.2 - The graph of the equation x2a2+y2b2=1 with a b 0...Ch. 11.2 - The graph of the equation x2b2+y2a2=1 with a b 0...Ch. 11.2 - Label the vertices and foci on the graphs given...Ch. 11.2 - Graphs of Ellipses Match the equation with the...Ch. 11.2 - Prob. 6ECh. 11.2 - Graphs of Ellipses Match the equation with the...Ch. 11.2 - Prob. 8ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 13ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 18ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 32ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 51ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.2 - Prob. 57ECh. 11.2 - Intersecting Ellipses Find the intersection points...Ch. 11.2 - Prob. 59ECh. 11.2 - Prob. 60ECh. 11.2 - Ancillary Circle The ancillary circle of an...Ch. 11.2 - Prob. 62ECh. 11.2 - Family of Ellipses If k 0, the following equation...Ch. 11.2 - How Wide Is an Ellipse at a Focus? A latus rectum...Ch. 11.2 - Perihelion and Aphelion The planets move around...Ch. 11.2 - The Orbit of Pluto With an eccentricity of 0.25,...Ch. 11.2 - Lunar Orbit For an object in an elliptical orbit...Ch. 11.2 - Plywood Ellipse A carpenter wishes to construct an...Ch. 11.2 - Sunburst Window A sunburst window above a doorway...Ch. 11.2 - DISCUSS: Drawing an Ellipse on a Blackboard Try...Ch. 11.2 - DISCUSS: Light Cone from a Flashlight A flashlight...Ch. 11.2 - DISCUSS: Is It an Ellipse? A piece of paper is...Ch. 11.3 - A hyperbola is the set of all points in the plane...Ch. 11.3 - The graph of the equation x2a2y2b2=1 with a 0, b ...Ch. 11.3 - Prob. 3ECh. 11.3 - Label the vertices, foci, and asymptotes on the...Ch. 11.3 - Graphs of Hyperbolas Match the equation with the...Ch. 11.3 - Prob. 6ECh. 11.3 - Graphs of Hyperbolas Match the equation with the...Ch. 11.3 - Prob. 8ECh. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Prob. 10ECh. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 38ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 40ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - Perpendicular Asymptotes (a) Show that the...Ch. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - Prob. 55ECh. 11.3 - Navigation In the figure on the next page, the...Ch. 11.3 - Comet Trajectories Some comets, such as Halleys...Ch. 11.3 - Ripples in Pool Two stones are dropped...Ch. 11.3 - Prob. 59ECh. 11.3 - DISCUSS: Light from a Lamp The light from a lamp...Ch. 11.4 - Prob. 1ECh. 11.4 - The graphs of x2 = 12y and (x 3)2 = 12(y 1) are...Ch. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Prob. 12ECh. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Prob. 20ECh. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Prob. 46ECh. 11.4 - Prob. 47ECh. 11.4 - Prob. 48ECh. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Prob. 50ECh. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Prob. 52ECh. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Prob. 55ECh. 11.4 - Prob. 56ECh. 11.4 - Prob. 57ECh. 11.4 - Prob. 58ECh. 11.4 - Prob. 59ECh. 11.4 - Prob. 60ECh. 11.4 - Prob. 61ECh. 11.4 - Prob. 62ECh. 11.4 - Prob. 63ECh. 11.4 - Prob. 64ECh. 11.4 - Prob. 65ECh. 11.4 - Path of a Cannonball A cannon fires a cannonball...Ch. 11.4 - Orbit of a Satellite A satellite is in an...Ch. 11.4 - Prob. 68ECh. 11.5 - Suppose the x- and y-axes are rotated through an...Ch. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Rotation of Axes Determine the XY-coordinates of...Ch. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 18ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Prob. 23ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 26ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 29ECh. 11.5 - Prob. 30ECh. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - Identifying a Hyperbola Using Rotation of Axes (a)...Ch. 11.5 - Prob. 34ECh. 11.5 - Prob. 35ECh. 11.5 - Prob. 36ECh. 11.5 - Prob. 37ECh. 11.5 - Prob. 38ECh. 11.5 - DISCOVER PROVE: Geometric Invariants Do you...Ch. 11.6 - Prob. 1ECh. 11.6 - Prob. 2ECh. 11.6 - Prob. 3ECh. 11.6 - Prob. 4ECh. 11.6 - Prob. 5ECh. 11.6 - Prob. 6ECh. 11.6 - Prob. 7ECh. 11.6 - Prob. 8ECh. 11.6 - Prob. 9ECh. 11.6 - Prob. 10ECh. 11.6 - Prob. 11ECh. 11.6 - Prob. 12ECh. 11.6 - Prob. 13ECh. 11.6 - Prob. 14ECh. 11.6 - Prob. 15ECh. 11.6 - Prob. 16ECh. 11.6 - Prob. 17ECh. 11.6 - Prob. 18ECh. 11.6 - Prob. 19ECh. 11.6 - Prob. 20ECh. 11.6 - Prob. 21ECh. 11.6 - Prob. 22ECh. 11.6 - Prob. 23ECh. 11.6 - Prob. 24ECh. 11.6 - Prob. 25ECh. 11.6 - Prob. 26ECh. 11.6 - Prob. 27ECh. 11.6 - Prob. 28ECh. 11.6 - Prob. 29ECh. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Prob. 32ECh. 11.6 - Prob. 33ECh. 11.6 - Prob. 34ECh. 11.6 - Prob. 35ECh. 11.6 - Prob. 36ECh. 11.6 - Prob. 37ECh. 11.6 - Prob. 38ECh. 11.6 - Prob. 39ECh. 11.6 - Prob. 40ECh. 11.6 - Prob. 41ECh. 11.6 - Prob. 42ECh. 11.6 - Prob. 43ECh. 11.6 - Perihelion and Aphelion The planets move around...Ch. 11.6 - Prob. 45ECh. 11.6 - Prob. 46ECh. 11.6 - Prob. 47ECh. 11 - (a) Give the geometric definition of a parabola....Ch. 11 - Prob. 2RCCCh. 11 - (a) Give the geometric definition of a hyperbola....Ch. 11 - Prob. 4RCCCh. 11 - Prob. 5RCCCh. 11 - Prob. 6RCCCh. 11 - Prob. 7RCCCh. 11 - Prob. 8RCCCh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Prob. 40RECh. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Prob. 44RECh. 11 - Prob. 45RECh. 11 - Prob. 46RECh. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Prob. 48RECh. 11 - Prob. 49RECh. 11 - Prob. 50RECh. 11 - Prob. 51RECh. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Prob. 56RECh. 11 - Prob. 57RECh. 11 - Prob. 58RECh. 11 - Prob. 59RECh. 11 - Prob. 60RECh. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Prob. 62RECh. 11 - Prob. 63RECh. 11 - Prob. 64RECh. 11 - Path of the Earth The path of the earth around the...Ch. 11 - LORAN A ship is located 40 mi from a straight...Ch. 11 - Prob. 67RECh. 11 - Prob. 68RECh. 11 - Prob. 69RECh. 11 - Prob. 70RECh. 11 - Prob. 71RECh. 11 - Prob. 72RECh. 11 - Prob. 73RECh. 11 - Prob. 74RECh. 11 - Prob. 75RECh. 11 - Prob. 76RECh. 11 - Prob. 77RECh. 11 - Prob. 78RECh. 11 - Prob. 79RECh. 11 - Prob. 80RECh. 11 - Find the focus and directrix of the parabola x2 =...Ch. 11 - Prob. 2TCh. 11 - Find the vertices, foci, and asymptotes of the...Ch. 11 - Prob. 4TCh. 11 - Prob. 5TCh. 11 - Prob. 6TCh. 11 - Prob. 7TCh. 11 - Prob. 8TCh. 11 - Prob. 9TCh. 11 - Determine whether the equation represents an...Ch. 11 - Determine whether the equation represents an...Ch. 11 - Prob. 12TCh. 11 - Prob. 13TCh. 11 - Find an equation for the parabola with focus (2,...Ch. 11 - A parabolic reflector for a car headlight forms a...Ch. 11 - (a) Use the discriminant to determine whether the...Ch. 11 - Prob. 17TCh. 11 - Conics in Architecture The photographs on page 836...Ch. 11 - Constructing a Hyperbola In this problem we...Ch. 11 - Prob. 3PCh. 11 - Prob. 4PCh. 11 - Tangent Lines to a Parabola In this problem we...Ch. 11 - Prob. 6P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Searchlight reflectors A parabolic mirror reflect light in a beam when the light source is placed at its focus. In the illustration, how far from the vertex of the parabolic reflector should the light source be placed? All the measurements are in the feetarrow_forwardPlywood Ellipse A carpenter wishes to construct an elliptical table top from a 4 ft by 8 ft sheet of plywood. He will trace out the ellipse using the “thumbtack and string” method illustrated in Figures 2 and 3. What length of string should he use, and how far apart should the tacks be located, if the ellipse is to be the largest possible that can be cut out of the plywood sheet?arrow_forwardDISCUSS: Is It an Ellipse? A piece of paper is wrapped around a cylindrical bottle, and then a compass is used to draw a circle on the paper, as shown in the figure. When the paper is laid flat, is the shape drawn on the paper an ellipse? (You don’t need to prove your answer, but you might want to do the experiment and see what you get.)arrow_forward
- A parabolic reflector for a car headlight forms a bowl shape that is 6 in. wide at its opening and 3 in. deep, as shown in the figure at the left. How far from the vertex should the filament of the bulb be placed if it is to be located at the focus?arrow_forwardFind the equation of the ellipse shown.arrow_forwardArchitecture A mason is building a semielliptical fireplace arch that has a height of 2 feet at the center and a width of 6 feet along the base (see figure). The mason draws the semiellipse on the wall by the method shown in Figure 4.22 on page 330. Find the positions of the thumbtacks and the length of the string.arrow_forward
- Statuary Hall is an elliptical room in the United States Capitol in Washington, D.C. The room is also called the Whispering Gallery because a person standing at one focus of the room can hear even a whisper spoken by a person standing at the other focus. This occurs because any sound emitted from one focus of an ellipse reflects off the side of the ellipse to the other focus. Statuary Hall is 46 feet wide and 97 feet long. (a) Find an equation that models the shape of the room. (b) How far apart are the two foci? (c) What is the area of the floor of the room? (The area of an ellipse is A=ab.)arrow_forwardReflecting Telescope The Hale telescope at the Mount Palomar Observatory has a 200-in. mirror, as shown in the figure. The mirror is constructed in a parabolic shape that collects light from the stars and focuses it at the prime focus, that is, the focus of the parabola. The mirror is 3.79 in. deep at its center. Find the focal length of this parabolic mirror, that is, the distance from the vertex to the focus.arrow_forwardSatellite Dish A reflector for a satellite dish is parabolic in cross section, with the receiver at the focus F. The reflector is 1 ft deep and 20 ft wide from rim to rim (see the figure). How far is the receiver from the vertex of the parabolic reflector?arrow_forward
- The parabolic cable of a suspension bridge is 50 feet above the roadbed at the ends of the bridge and is 10 feet above it at the center of the bridge. [See the diagram below. ] The vertical support cables that are drawn are evenly spaced every 20 feet along the bridge. 50 feet 10 feet high 340 feet Write down the equation of the parabola. Notice that the x-axis and y-axis are already drawn in the figure. Show all work. Give exact answers, or decimals accurate to at least 6 decimal places. Calculate the length of the vertical support cable that is marked with a "w" in the diagram. Show your work. Give answer accurate to 2 decimal places. a) b)arrow_forwardClaude has a piece of cheese in the shape of a cone. He uses a straight cut to slice off a smaller piece. Which shape could be one of the faces of Claude's smaller piece of cheese? A. Ellipse B. Square C. Pentagon D. Paralleloaram OA ODarrow_forwardHow are the graphs of these ellipses similar, and how are they different? y? = 1 y? 1 36 144 36 144arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
What is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY