Explanation Formula used: The distance between point P ( x 1 , y 1 ) and the point Q ( x 2 , y 2 ) is obtained by distance formula d = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 The distance between the point P ( x 0 , y 0 ) and the line a x + b y + c = 0 is obtained by formula. d = | a ( x 0 ) + b ( y 0 ) + c | a 2 + b 2 Calculation: According to the statement in the question, the distance between point P ( x , y ) and the point ( 5 , 4 ) is 5 3 of the distance between P ( x , y ) and the line x = − 3 as shown in figure 1. From the figure and condition the mathematical modelled equation is P B = 5 3 A P . ( x − 5 ) 2 + ( y − 4 ) 2 = 5 3 | 1 ( x ) + 0 ( y ) + 3 | 1 2 + 0 2 ( x − 5 ) 2 + ( y − 4 ) 2 = 5 3 | x + 3 | 1 ( x − 5 ) 2 + ( y − 4 ) 2 = 5 3 | x + 3 | Take square on both sides of the equation and solve further as below: ( ( x − 5 ) 2 + ( y − 4 ) 2 ) 2 = ( 5 3 | x + 3 | ) 2 ( x − 5 ) 2 + ( y − 4 ) 2 = 5 2 3 2 ( x + 3 ) 2 3 2 ( x − 5 ) 2 + 3 2 ( y − 4 ) 2 = 5 2 ( x + 3 ) 2 9 { x 2 + 25 − 10 x } + 9 { y 2 + 16 − 8 y } = 25 { x 2 + 9 + 6 x } Further, solve the above equation

WebAssign with Corequisite Support for Gustafson/Hughes' College Algebra, 12th Edition [Instant Access], Single-Term

12th Edition

ISBN: 9780357422533

Author: Gustafson; R. David; Hughes; Jeff

Publisher: Cengage Learning US

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Chapter 7.3, Problem 54E

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The equation in standard form of the hyperbola of the condition that distance between point P(x,y) and the point (5,4) is 53 of the distance between P and the line x=−3.

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Chapter 7.3, Problem 53E

Chapter 7.3, Problem 55E

Chapter 7 Solutions

WebAssign with Corequisite Support for Gustafson/Hughes' College Algebra, 12th Edition [Instant Access], Single-Term

Ch. 7.1 - Prob. 1SC Ch. 7.1 - Prob. 2SC Ch. 7.1 - Prob. 3SC Ch. 7.1 - Prob. 4SC Ch. 7.1 - Prob. 5SC Ch. 7.1 - Prob. 6SC Ch. 7.1 - Find the vertex and yintercepts of the parabola...Ch. 7.1 - Prob. 8SC Ch. 7.1 - Prob. 9SC Ch. 7.1 - Prob. 1E

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The equation in standard form of the hyperbola of the condition that distance between point P ( x , y ) and the point ( 5 , 4 ) is 5 3 of the distance between P and the line x = − 3 .

Solution Summary: The author explains the equation in standard form of the hyperbola that satisfies the condition that distance between point P(x,y) and the line x=-3.

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To Find:

The equation in standard form of the hyperbola of the condition that distance between point P(x,y) and the point (5,4) is 53 of the distance between P and the line x=−3.

Want to see the full answer?

Chapter 7 Solutions

The equation in standard form of the hyperbola of the condition that distance between point P ( x , y ) and the point ( 5 , 4 ) is 5 3 of the distance between P and the line x = − 3 .

Solution Summary: The author explains the equation in standard form of the hyperbola that satisfies the condition that distance between point P(x,y) and the line x=-3.

Videos

To Find: The equation in standard form of the hyperbola of the condition that distance between point P(x,y) and the point (5,4) is 53 of the distance between P and the line x=−3.

Want to see the full answer?

Chapter 7 Solutions

To Find:

The equation in standard form of the hyperbola of the condition that distance between point P(x,y) and the point (5,4) is 53 of the distance between P and the line x=−3.