PRECALCULUS >CUSTOM<
7th Edition
ISBN: 9781337037785
Author: Stewart
Publisher: CENGAGE C
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Chapter 11.2, Problem 56E
To determine
To find: The equation of the ellipse with eccentricity
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Chapter 11 Solutions
PRECALCULUS >CUSTOM<
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
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- 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_forwardDefine an ellipse in terms of its foci.arrow_forwardWhat special case of the ellipse do we have when the major and minor axis are of the same length?arrow_forward
- An arch has the shape of a semi-ellipse. The arch has a height of 12 feet and a span of 40 feet. Find an equation for the ellipse, and use that to find the distance from the center to a point at which the height is 6 feet. Round to the nearest hundredth.arrow_forwardAn arch has the shape of a semi-ellipse (the top half of an ellipse). The arch has a height of 8 feet and a span of 20 feet. Find an equation for the ellipse, and use that to find the height to the nearest 0.01 foot of the arch at a distance of 4 feet from the center.arrow_forwardFind an equation for the ellipse with center (2, 0), foci (2,3) and major axis of length 8.arrow_forward
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What is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY