Explanation Given info: Equation of parabola y = x 2 Co-ordinate of P = ( 0 , 1 4 ) Equation of line y = − 1 4 Concept used: Distance formula between P ( x 1 , y 1 ) and Q ( x 2 , y 2 ) P Q = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 Distance between line y = c and the point ( x 1 , y 1 ) is | y 1 − y | Calculation: Let x − coordinate of given point = x Then by equation of parabola y − coordinate y = x 2 Co-ordinate of general point ( x , x 2 ) and coordinate of the point F= ( 0 , 1 4 ) FP (Distance between F and P points) = ( x − 0 ) 2 + ( x 2 − 1 4 ) 2 = x + 2 ( x 2 − 1 4 ) 2 ( a − b ) 2 = a 2 − 2 a b + b 2 = x 2 + x 4 − <

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 1.2, Problem 54E

To determine

Show that the parabola y=x2 consists of all points P such that d1=d2 where d1 is the distance from p to (0,14) and d2 is the distance from P to the line y=−14

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Chapter 1.2, Problem 53E

Chapter 1.2, Problem 55E

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Chapter 1 Solutions

Calculus - Standalone book

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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Show that the parabola y = x 2 consists of all points P such that d 1 = d 2 where d 1 is the distance from p to ( 0 , 1 4 ) and d 2 is the distance from P to the line y = − 1 4

Solution Summary: The author explains that the parabola y=x2 consists of all points P.

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Show that the parabola y=x2 consists of all points P such that d1=d2 where d1 is the distance from p to (0,14) and d2 is the distance from P to the line y=−14

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Chapter 1 Solutions