Explanation Given: The sum of the distance from the two foci ( − c , 0 ) and ( c , 0 ) to any point on the ellipse ( x , y ) is 2 a . Calculation: Given that, b 2 = c 2 − a 2 . That is, a 2 − c 2 = − b 2 . Simplify the given equation ( x + c ) 2 + y 2 − ( x − c ) 2 + y 2 = 2 a as follows. ( x + c ) 2 + y 2 − ( x − c ) 2 + y 2 = 2 a ( x + c ) 2 + y 2 = 2 a + ( x − c ) 2 + y 2 Squaring on the both sides of the above expression as follows. ( ( x + c ) 2 + y 2 ) 2 = ( 2 a + ( x − c ) 2 + y 2 ) 2 ( x + c ) 2 + y 2 = ( 2 a ) 2 + ( ( x − c ) 2 + y 2 ) 2 + 2 ( 2 a ( x − c ) 2 + y 2 ) x 2 + c 2 + 2 x c + y 2 = 4 a 2 + ( ( x − c ) 2 + y 2 ) + 4 a ( x − c ) 2 + y 2 x 2 + c 2 + 2 x c + y 2 = 4 a 2 + ( x 2 + c 2 − 2 x c ) + y 2 + 4 a ( x − c ) 2 + y 2 On further simplification, x 2 − x 2 + c 2 − c 2 + 2 x c + 2 x c − 4 a 2 + y 2 − y 2 = 4 a ( x − c ) 2 + y 2 4 x c − 4 a 2 = 4 a ( x − c ) 2 + y 2 x c − a 2 = a ( x − c ) 2 + y 2 Squaring on the both sides of the above expression as follows

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

5th Edition

ISBN: 9780134179025

Author: Ronald J. Harshbarger, Lisa S. Yocco

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 8.8, Problem 54E

To determine

To show: The equation (x+c)2+y2−(x−c)2+y2=2a can be written as x2a2−y2b2=1 if b2=c2−a2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.8, Problem 53E

Chapter 8, Problem 1RE

Chapter 8 Solutions

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

Ch. 8.1 - In Exercises 16, graph each inequality. 1. y 5x ...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - In Exercises 710, match each solution of a system...Ch. 8.1 - Prob. 10E

Ch. 8.1 - Prob. 11E Ch. 8.1 - In Exercises 1116, the graph of the boundary...Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - For each system of inequalities in Exercises 1722,...Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - In Exercises 2326, graph the solution of the...Ch. 8.1 - Prob. 25E Ch. 8.1 - In Exercises 2326, graph the solution of the...Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Sales Trix Auto Sales sells used cars. To promote...Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Manufacturing A company manufactures two types of...Ch. 8.1 - Prob. 34E Ch. 8.1 - Production A firm produces three different-size...Ch. 8.1 - Advertising Tire Town is developing an advertising...Ch. 8.1 - Nutrition A privately owned lake contains two...Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Manufacturing Safeco Company produces two types of...Ch. 8.1 - Manufacturing A company manufactures commercial...Ch. 8.1 - Constructing a Box An open box with a square base...Ch. 8.2 - In Exercises 1-4, use the given feasible region...Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Find the maximum possible value of f = 400x + 300y...Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Find the maximum possible value of f = 80x + 160y...Ch. 8.2 - Prob. 12E Ch. 8.2 - Find the minimum possible value of g = 40x + 30y...Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Manufacturing A company manufactures two types of...Ch. 8.2 - Manufacturing Evergreen Company produces two types...Ch. 8.2 - Prob. 21E Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Politics A political candidate wishes to use a...Ch. 8.2 - Prob. 31E Ch. 8.2 - Manufacturing Kitchen Pride manufactures toasters...Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Find the first 5 terms of the sequence defined by...Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Salaries Suppose you are offered a job with a...Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Bouncing Ball A ball is dropped from 128 feet. It...Ch. 8.4 - Find the sum of the first 6 terms of the geometric...Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Find the sum of the first 20 terms of the...Ch. 8.4 - Find the sum of the first 15 terms of the...Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - Prob. 10E Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Salaries Suppose you are offered two identical...Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - Prob. 31E Ch. 8.4 - Email Chain Letters Suppose the email chain letter...Ch. 8.4 - Prob. 33E Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.4 - Prob. 36E Ch. 8.4 - Prob. 37E Ch. 8.4 - Prob. 38E Ch. 8.4 - Prob. 39E Ch. 8.4 - Prob. 40E Ch. 8.4 - Prob. 41E Ch. 8.5 - Prob. 1E Ch. 8.5 - Prob. 2E Ch. 8.5 - Prob. 3E Ch. 8.5 - Prob. 4E Ch. 8.5 - Prob. 5E Ch. 8.5 - Prob. 6E Ch. 8.5 - Prob. 7E Ch. 8.5 - Prob. 8E Ch. 8.5 - Prob. 9E Ch. 8.5 - Prob. 10E Ch. 8.5 - Prob. 11E Ch. 8.5 - Prob. 12E Ch. 8.5 - Prob. 13E Ch. 8.5 - Prob. 14E Ch. 8.5 - Prob. 15E Ch. 8.5 - Prob. 16E Ch. 8.5 - Prob. 17E Ch. 8.5 - Prob. 18E Ch. 8.5 - Prob. 19E Ch. 8.5 - Prob. 20E Ch. 8.5 - Prob. 21E Ch. 8.5 - Prob. 22E Ch. 8.5 - Prob. 23E Ch. 8.5 - Prob. 24E Ch. 8.5 - Prob. 25E Ch. 8.5 - Prob. 26E Ch. 8.5 - Prob. 27E Ch. 8.5 - Prob. 28E Ch. 8.5 - Prob. 29E Ch. 8.5 - Prob. 30E Ch. 8.5 - Prob. 31E Ch. 8.5 - Prob. 32E Ch. 8.5 - Prob. 33E Ch. 8.5 - Prob. 34E Ch. 8.5 - Prob. 35E Ch. 8.5 - Prob. 36E Ch. 8.5 - Prob. 37E Ch. 8.5 - Prob. 38E Ch. 8.5 - Prob. 39E Ch. 8.5 - Prob. 40E Ch. 8.5 - Prob. 41E Ch. 8.5 - Prob. 42E Ch. 8.5 - Prob. 43E Ch. 8.5 - Prob. 44E Ch. 8.5 - Prob. 45E Ch. 8.5 - Prob. 46E Ch. 8.5 - Prob. 47E Ch. 8.5 - Prob. 48E Ch. 8.5 - Prob. 49E Ch. 8.5 - Prob. 50E Ch. 8.5 - Prob. 51E Ch. 8.5 - Prob. 52E Ch. 8.5 - Prob. 53E Ch. 8.5 - Prob. 54E Ch. 8.5 - Prob. 55E Ch. 8.5 - Prob. 56E Ch. 8.6 - Prob. 1E Ch. 8.6 - Prob. 2E Ch. 8.6 - Prob. 3E Ch. 8.6 - Prob. 4E Ch. 8.6 - Prob. 5E Ch. 8.6 - Prob. 6E Ch. 8.6 - Prob. 7E Ch. 8.6 - Prob. 8E Ch. 8.6 - Prob. 9E Ch. 8.6 - Prob. 10E Ch. 8.6 - Prob. 11E Ch. 8.6 - Prob. 12E Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 14E Ch. 8.6 - Prob. 15E Ch. 8.6 - Prob. 16E Ch. 8.6 - Prob. 17E Ch. 8.6 - Prob. 18E Ch. 8.6 - Prob. 19E Ch. 8.6 - Prob. 20E Ch. 8.6 - Prob. 21E Ch. 8.6 - Prob. 22E Ch. 8.6 - Prob. 23E Ch. 8.6 - Expand the following binomial powers. 24. (x y)7 Ch. 8.6 - Prob. 25E Ch. 8.6 - Prob. 26E Ch. 8.6 - Prob. 27E Ch. 8.6 - Prob. 28E Ch. 8.6 - Prob. 29E Ch. 8.6 - Prob. 30E Ch. 8.6 - Prob. 31E Ch. 8.6 - Prob. 32E Ch. 8.6 - Prob. 33E Ch. 8.6 - Prob. 34E Ch. 8.7 - Prob. 1E Ch. 8.7 - Prob. 2E Ch. 8.7 - Prob. 3E Ch. 8.7 - Prob. 4E Ch. 8.7 - Prob. 5E Ch. 8.7 - Prob. 6E Ch. 8.7 - Prob. 7E Ch. 8.7 - Prob. 8E Ch. 8.7 - Prob. 9E Ch. 8.7 - Prob. 10E Ch. 8.7 - Prob. 11E Ch. 8.7 - Prob. 12E Ch. 8.7 - Prob. 13E Ch. 8.7 - Prob. 14E Ch. 8.7 - Prob. 15E Ch. 8.7 - Prob. 16E Ch. 8.7 - Prob. 17E Ch. 8.7 - Prob. 18E Ch. 8.7 - Prob. 19E Ch. 8.7 - Prob. 20E Ch. 8.7 - Prob. 21E Ch. 8.7 - Prob. 22E Ch. 8.7 - Prob. 23E Ch. 8.7 - Prob. 24E Ch. 8.7 - Prob. 25E Ch. 8.7 - Prob. 26E Ch. 8.7 - Prob. 27E Ch. 8.7 - Prob. 28E Ch. 8.7 - Prob. 29E Ch. 8.7 - Prob. 30E Ch. 8.7 - Prob. 31E Ch. 8.7 - Prob. 32E Ch. 8.7 - Prob. 33E Ch. 8.7 - Prob. 34E Ch. 8.7 - Prob. 35E Ch. 8.7 - In Exercises 3336, write the equation of the shape...Ch. 8.7 - Prob. 37E Ch. 8.7 - Prob. 38E Ch. 8.7 - Write the equation of the circle that is tangent...Ch. 8.7 - Prob. 40E Ch. 8.7 - Prob. 41E Ch. 8.7 - Prob. 42E Ch. 8.7 - Prob. 43E Ch. 8.7 - Prob. 44E Ch. 8.7 - Prob. 45E Ch. 8.7 - Prob. 46E Ch. 8.7 - Prob. 47E Ch. 8.7 - Prob. 48E Ch. 8.7 - Prob. 49E Ch. 8.7 - Prob. 50E Ch. 8.7 - Prob. 51E Ch. 8.7 - Prob. 52E Ch. 8.7 - Prob. 53E Ch. 8.7 - Prob. 54E Ch. 8.7 - In Exercises 4160, graph each equation. 55. 4x2 +...Ch. 8.7 - Prob. 56E Ch. 8.7 - Prob. 57E Ch. 8.7 - Prob. 58E Ch. 8.7 - Prob. 59E Ch. 8.7 - Prob. 60E Ch. 8.7 - Bridges A cable of a suspension bridge is...Ch. 8.7 - Prob. 62E Ch. 8.7 - Prob. 63E Ch. 8.7 - Prob. 64E Ch. 8.8 - Prob. 1E Ch. 8.8 - Prob. 2E Ch. 8.8 - Prob. 3E Ch. 8.8 - Prob. 4E Ch. 8.8 - Prob. 5E Ch. 8.8 - Prob. 6E Ch. 8.8 - Prob. 7E Ch. 8.8 - Prob. 8E Ch. 8.8 - Prob. 9E Ch. 8.8 - Prob. 10E Ch. 8.8 - Prob. 11E Ch. 8.8 - Prob. 12E Ch. 8.8 - Prob. 13E Ch. 8.8 - Prob. 14E Ch. 8.8 - Prob. 15E Ch. 8.8 - Prob. 16E Ch. 8.8 - Prob. 17E Ch. 8.8 - Prob. 18E Ch. 8.8 - Prob. 19E Ch. 8.8 - Prob. 20E Ch. 8.8 - Sketch the graph of the ellipse with center at (0,...Ch. 8.8 - Prob. 22E Ch. 8.8 - Prob. 23E Ch. 8.8 - Prob. 24E Ch. 8.8 - Prob. 25E Ch. 8.8 - Prob. 26E Ch. 8.8 - Prob. 27E Ch. 8.8 - Prob. 28E Ch. 8.8 - Prob. 29E Ch. 8.8 - Prob. 30E Ch. 8.8 - Prob. 31E Ch. 8.8 - Prob. 32E Ch. 8.8 - Prob. 33E Ch. 8.8 - Prob. 34E Ch. 8.8 - Prob. 35E Ch. 8.8 - Prob. 36E Ch. 8.8 - Prob. 37E Ch. 8.8 - Prob. 38E Ch. 8.8 - Prob. 39E Ch. 8.8 - Prob. 40E Ch. 8.8 - Prob. 41E Ch. 8.8 - Prob. 42E Ch. 8.8 - Prob. 43E Ch. 8.8 - Prob. 44E Ch. 8.8 - Prob. 45E Ch. 8.8 - Prob. 46E Ch. 8.8 - Prob. 47E Ch. 8.8 - Prob. 48E Ch. 8.8 - Prob. 49E Ch. 8.8 - Prob. 50E Ch. 8.8 - Prob. 51E Ch. 8.8 - Prob. 52E Ch. 8.8 - Prob. 53E Ch. 8.8 - Prob. 54E Ch. 8 - Prob. 1RE Ch. 8 - Prob. 2RE Ch. 8 - Prob. 3RE Ch. 8 - Prob. 4RE Ch. 8 - Prob. 5RE Ch. 8 - Prob. 6RE Ch. 8 - Prob. 7RE Ch. 8 - Prob. 8RE Ch. 8 - Prob. 9RE Ch. 8 - Prob. 10RE Ch. 8 - Prob. 11RE Ch. 8 - Prob. 12RE Ch. 8 - Prob. 13RE Ch. 8 - Prob. 14RE Ch. 8 - Prob. 15RE Ch. 8 - Prob. 16RE Ch. 8 - Prob. 17RE Ch. 8 - Find the sum of the first 12 terms of the sequence...Ch. 8 - Prob. 19RE Ch. 8 - Prob. 20RE Ch. 8 - Prob. 21RE Ch. 8 - Prob. 22RE Ch. 8 - Write f(x) = 8x3 + 5x1 + 4x with no negative...Ch. 8 - Prob. 24RE Ch. 8 - Prob. 25RE Ch. 8 - Prob. 26RE Ch. 8 - Prob. 27RE Ch. 8 - Prob. 28RE Ch. 8 - Prob. 29RE Ch. 8 - Prob. 30RE Ch. 8 - Prob. 31RE Ch. 8 - Prob. 32RE Ch. 8 - Prob. 33RE Ch. 8 - Prob. 34RE Ch. 8 - Prob. 35RE Ch. 8 - Prob. 36RE Ch. 8 - Prob. 37RE Ch. 8 - Prob. 38RE Ch. 8 - Prob. 39RE Ch. 8 - Prob. 40RE Ch. 8 - Prob. 41RE Ch. 8 - Prob. 42RE Ch. 8 - Prob. 43RE Ch. 8 - Manufacturing Ace Manufacturing produces two types...Ch. 8 - Prob. 45RE Ch. 8 - Prob. 46RE Ch. 8 - Manufacturing A company manufactures leaf blowers...Ch. 8 - Profits A woman has a building with 60 two-bedroom...Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - Prob. 54RE Ch. 8 - Prob. 55RE Ch. 8 - Bridges The towers of a suspension bridge are 800...Ch. 8 - Prob. 57RE Ch. 8 - Prob. 58RE

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

Recommended textbooks for you

College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
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

College Algebra

Algebra

ISBN:9781337282291

Author:Ron Larson

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

SEE MORE TEXTBOOKS

08 - Conic Sections - Hyperbolas, Part 1 (Graphing, Asymptotes, Hyperbola Equation, Focus); Author: Math and Science;https://www.youtube.com/watch?v=Ryj0DcdGPXo;License: Standard YouTube License, CC-BY

The equation ( x + c ) 2 + y 2 − ( x − c ) 2 + y 2 = 2 a can be written as x 2 a 2 − y 2 b 2 = 1 if b 2 = c 2 − a 2 .

Solution Summary: The author explains how the given equation sqrt(x+c)2+y 2=2a can be written.

Videos

To show: The equation (x+c)2+y2−(x−c)2+y2=2a can be written as x2a2−y2b2=1 if b2=c2−a2.

Want to see the full answer?

Chapter 8 Solutions