College Algebra
10th Edition
ISBN: 9781337282291
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 4.3, Problem 92E
To determine
The condition for ellipse when it is
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Chapter 4 Solutions
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Ch. 4.1 - Finding the Domain of a Rational Function In...Ch. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Finding the Domain of a Rational Function In...Ch. 4.1 - Finding the Domain of a Rational Function In...Ch. 4.1 - Finding the Domain of a Rational Function In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Prob. 20ECh. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Finding Vertical and Horizontal Asymptotes In...Ch. 4.1 - Matching In Exercises 29-36, match the rational...Ch. 4.1 - Matching In Exercises 29-36, match the rational...Ch. 4.1 - Matching In Exercises 29-36, match the rational...Ch. 4.1 - Matching In Exercises 29-36, match the rational...Ch. 4.1 - Matching In Exercises 29-36, match the rational...Ch. 4.1 - Matching In Exercises 29-36, match the rational...Ch. 4.1 - Matching In Exercises 29-36, match the rational...Ch. 4.1 - Matching In Exercises 29-36, match the rational...Ch. 4.1 - Numerical Analysis In Exercises 37-40, In this...Ch. 4.1 - Numerical Analysis In Exercises 37-40, In this...Ch. 4.1 - Prob. 39ECh. 4.1 - Numerical Analysis In Exercises 37-40, In this...Ch. 4.1 - Recycling The cost C (in dollars) of supplying...Ch. 4.1 - Ecology The cost C (in millions of dollars) of...Ch. 4.1 - Population Growth The game commission introduces...Ch. 4.1 - Biology A science class performs an experiment...Ch. 4.1 - Psychologists have developed mathematical models...Ch. 4.1 - Physics Experiment Consider a physics laboratory...Ch. 4.1 - The graph of a polynomial function can have...Ch. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - The graph of a rational function f(x)=N(x)D(x)is...Ch. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.2 - Sketch the graph of f(x)=1x+3and state its domain.Ch. 4.2 - Prob. 2ECPCh. 4.2 - Prob. 3ECPCh. 4.2 - Prob. 4ECPCh. 4.2 - Prob. 5ECPCh. 4.2 - Prob. 6ECPCh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 16ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 18ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 20ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 22ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 24ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 26ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 34ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 36ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Sketching the Graph of a Rational Function In...Ch. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - A Rational Function with a Slant Asymptote In...Ch. 4.2 - Prob. 50ECh. 4.2 - In this question, (a) state the domain of the...Ch. 4.2 - Prob. 52ECh. 4.2 - In Exercises 47-62, (a) state the domain of the...Ch. 4.2 - In Exercises 47-62, (a) state the domain of the...Ch. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - Prob. 65ECh. 4.2 - Prob. 66ECh. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - Prob. 70ECh. 4.2 - Prob. 71ECh. 4.2 - Prob. 72ECh. 4.2 - Prob. 73ECh. 4.2 - Prob. 74ECh. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - Prob. 77ECh. 4.2 - Prob. 78ECh. 4.2 - Prob. 79ECh. 4.2 - Page Design A rectangular page contains 64square...Ch. 4.2 - A page that is x inches wide and y inches high...Ch. 4.2 - Concentration of a Mixture A 1000-liter tank...Ch. 4.2 - Prob. 83ECh. 4.2 - Prob. 84ECh. 4.2 - Prob. 85ECh. 4.2 - Prob. 86ECh. 4.2 - Prob. 87ECh. 4.2 - Prob. 88ECh. 4.2 - Average Speed A driver’s average speed is 50 miles...Ch. 4.2 - Medicine The concentration Cof a chemical in the...Ch. 4.2 - Prob. 91ECh. 4.2 - Prob. 92ECh. 4.2 - Prob. 93ECh. 4.2 - Prob. 94ECh. 4.2 - Prob. 95ECh. 4.2 - Prob. 96ECh. 4.2 - Writing and Graphing a Rational Function Write a...Ch. 4.2 - Prob. 98ECh. 4.2 - Prob. 99ECh. 4.3 - Find the focus and directrix of the parabola...Ch. 4.3 - Find the standard form of the equation of the...Ch. 4.3 - Prob. 3ECPCh. 4.3 - Prob. 4ECPCh. 4.3 - Prob. 5ECPCh. 4.3 - Prob. 6ECPCh. 4.3 - Prob. 7ECPCh. 4.3 - Fill in the blanks. A is the intersection of a...Ch. 4.3 - Prob. 2ECh. 4.3 - Fill in the blanks. A is the set of all points...Ch. 4.3 - Fill in the blanks. The line that passes through...Ch. 4.3 - Fill in the blanks. An is the set of all points...Ch. 4.3 - Fill in the blanks. The chord joining the vertices...Ch. 4.3 - Fill in the blanks. A is the set of all points...Ch. 4.3 - Fill in the blanks. The line segment connecting...Ch. 4.3 - Matching In Exercises 9-14, this question, match...Ch. 4.3 - Matching In Exercises 9-14, match the equation...Ch. 4.3 - Matching In Exercises 9-14, match the equation...Ch. 4.3 - Matching In Exercises 9-14, this question, match...Ch. 4.3 - Matching In Exercises 9-14, this question, match...Ch. 4.3 - Matching In Exercises 9-14, this question, match...Ch. 4.3 - Finding the Focus and Directrix of a Parabola In...Ch. 4.3 - Prob. 16ECh. 4.3 - Finding the Focus and Directrix of a Parabola In...Ch. 4.3 - Finding the Focus and Directrix of a Parabola In...Ch. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Finding the Standard Equation of a Parabola In...Ch. 4.3 - Finding the Standard Equation of a Parabola In...Ch. 4.3 - Finding the Standard Equation of a Parabola In...Ch. 4.3 - Finding the Standard Equation of a Parabola In...Ch. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - In Exercises 27 and 28, Find the standard form of...Ch. 4.3 - In Exercises 27 and 28, Find the standard form of...Ch. 4.3 - The light bulb in a flashlight is at the focus of...Ch. 4.3 - The receiver of a parabolic satellite dish is at...Ch. 4.3 - Suspension Bridge Each cable of the Golden Gate...Ch. 4.3 - Beam Deflection A simply supported beam (see...Ch. 4.3 - Finding the Standard Equation of an Ellipse In...Ch. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Finding the Standard Equation of an Ellipse In...Ch. 4.3 - Prob. 42ECh. 4.3 - Sketching an Ellipse In Exercises 43-52, find the...Ch. 4.3 - Prob. 44ECh. 4.3 - Sketching an Ellipse In Exercises 43-52, find the...Ch. 4.3 - Prob. 46ECh. 4.3 - Sketching an Ellipse In Exercises 43-52, find the...Ch. 4.3 - Prob. 48ECh. 4.3 - Sketching an Ellipse In Exercises 43-52, find the...Ch. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Architecture A mason is building a semielliptical...Ch. 4.3 - A semielliptical arch over a tunnel for a one-way...Ch. 4.3 - Prob. 57ECh. 4.3 - Geometry A line segment through a focus of an...Ch. 4.3 - Using Latera Recta In Exercises 59-62, sketch the...Ch. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Sketching a Hyperbola In Exercises 71-80, find the...Ch. 4.3 - Prob. 72ECh. 4.3 - Sketching a Hyperbola In Exercises 71-80, find the...Ch. 4.3 - Prob. 74ECh. 4.3 - Sketching a Hyperbola In Exercises 71-80, find the...Ch. 4.3 - Prob. 76ECh. 4.3 - Prob. 77ECh. 4.3 - Prob. 78ECh. 4.3 - Sketching a Hyperbola In Exercises 71-80, find the...Ch. 4.3 - Prob. 80ECh. 4.3 - Art A cross section of a sculpture can be modeled...Ch. 4.3 - Optics A hyperbolic mirror (used in some...Ch. 4.3 - When an airplane travels faster than the speed of...Ch. 4.3 - Navigation Long-distance radio navigation for...Ch. 4.3 - Prob. 85ECh. 4.3 - Prob. 86ECh. 4.3 - Prob. 87ECh. 4.3 - Prob. 88ECh. 4.3 - Area of an Ellipse Consider the ellipse...Ch. 4.3 - Prob. 90ECh. 4.3 - Prob. 91ECh. 4.3 - Prob. 92ECh. 4.3 - Prob. 93ECh. 4.3 - Prob. 94ECh. 4.3 - Prob. 95ECh. 4.3 - Prob. 96ECh. 4.3 - Drawing Ellipses Use two thumbtacks, a string, and...Ch. 4.3 - Prob. 98ECh. 4.3 - Prob. 99ECh. 4.4 - Identify each conic. Then describe the translation...Ch. 4.4 - Prob. 2ECPCh. 4.4 - Prob. 3ECPCh. 4.4 - Prob. 4ECPCh. 4.4 - Prob. 5ECPCh. 4.4 - Prob. 6ECPCh. 4.4 - Prob. 7ECPCh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Finding Characteristics of a Parabola In Exercises...Ch. 4.4 - Finding Characteristics of a Parabola In Exercises...Ch. 4.4 - Finding Characteristics of a Parabola In Exercises...Ch. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Finding Characteristics of a Parabola In Exercises...Ch. 4.4 - Prob. 34ECh. 4.4 - Finding the Standard Equation of a Parabola In...Ch. 4.4 - Finding the Standard Equation of a Parabola In...Ch. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Finding the Standard Equation of a Parabola In...Ch. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - Fluid Flow Water flowing from a horizontal pipe 48...Ch. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Prob. 45ECh. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - Prob. 50ECh. 4.4 - Prob. 51ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Prob. 56ECh. 4.4 - Finding the Standard Equation of an Ellipse In...Ch. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Planetary Motion The dwarf planet Pluto moves in...Ch. 4.4 - Australian Football In Australia, football by...Ch. 4.4 - Prob. 67ECh. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - Prob. 74ECh. 4.4 - Prob. 75ECh. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Prob. 78ECh. 4.4 - Prob. 79ECh. 4.4 - Prob. 80ECh. 4.4 - Prob. 81ECh. 4.4 - Prob. 82ECh. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Prob. 87ECh. 4.4 - Prob. 88ECh. 4.4 - Prob. 89ECh. 4.4 - Prob. 90ECh. 4.4 - Prob. 91ECh. 4.4 - Prob. 92ECh. 4.4 - Prob. 93ECh. 4.4 - Prob. 94ECh. 4.4 - Prob. 95ECh. 4 - Finding the Domain of a Rational Function In...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Finding Vertical and Horizontal Asymptotes In...Ch. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Seizure of Illegal Drugs The cost C(in millions of...Ch. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - The concentration C of a chemical in the...Ch. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Suspension Bridge Each cable of a suspension...Ch. 4 - Prob. 51RECh. 4 - Finding the Standard Equation of an Ellipse In...Ch. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Architecture A semi elliptical archway is formed...Ch. 4 - Wading Pool You are building a wading pool that is...Ch. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Finding the Standard Equation of an Ellipse In...Ch. 4 - Prob. 73RECh. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - Prob. 78RECh. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 82RECh. 4 - Prob. 83RECh. 4 - Prob. 84RECh. 4 - Architecture A parabolic archway is 12 meters high...Ch. 4 - Architecture A church window is bounded above by a...Ch. 4 - Running Path Let (0,0) represent a water fountain...Ch. 4 - Prob. 88RECh. 4 - Prob. 89RECh. 4 - Prob. 90RECh. 4 - In Exercises 1-3, find the domain of the function...Ch. 4 - In Exercises 1-3, find the domain of the function...Ch. 4 - In Exercises 1-3, find the domain of the function...Ch. 4 - Prob. 4TCh. 4 - In Exercises 4-9, identify any intercepts and...Ch. 4 - In Exercises 4-9, identify any intercepts and...Ch. 4 - In Exercises 4-9, identify any intercepts and...Ch. 4 - In Exercises 4-9, identify any intercepts and...Ch. 4 - In Exercises 4-9, identify any intercepts and...Ch. 4 - Prob. 10TCh. 4 - A triangle is formed by the coordinate axes and a...Ch. 4 - Prob. 12TCh. 4 - Sketch the conic and identify the center,...Ch. 4 - Prob. 14TCh. 4 - In Exercises 12-17, sketch the conic and identify...Ch. 4 - Prob. 16TCh. 4 - In Exercises 12-17, sketch the conic and identify...Ch. 4 - Find the standard form of the equation of the...Ch. 4 - Find the standard form of the equation of the...Ch. 4 - Prob. 20TCh. 4 - The moon orbits Earth in an elliptical path with...Ch. 4 - Match the graph of the rational function...Ch. 4 - Prob. 2PSCh. 4 - Distinct Vision The endpoints of the interval over...Ch. 4 - Statuary Hall is an elliptical room in the United...Ch. 4 - Property of a Hyperbola Use the figure to show...Ch. 4 - Prob. 6PSCh. 4 - Tour Boat A tour boat travels between two islands...Ch. 4 - The filament of a light bulb is a thin wire that...Ch. 4 - Prob. 9PSCh. 4 - Prob. 10PSCh. 4 - Prob. 11PS
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- Define an ellipse in terms of its foci.arrow_forwardStatuary 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_forwardFind the equation of the parabolic arch formed in the foundation of the bridge shown. Write the equation in standard form.arrow_forward
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