To determine Calculate the equation for the set of all points equidistant from the planes y = 3 and y = − 1 . Explanation Given information: The planes are y = 3 and y = − 1 . Formula used: Write the general expression to calculate the distance between P 1 ( x 1 , y 1 , z 1 ) and P 2 ( x 2 , y 2 , z 2 ) is, | P 1 P 2 | = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 + ( z 2 − z 1 ) 2 (1) Calculation: The point representation for the given planes are ( x , 3 , z ) and ( x , − 1 , z ) . Apply the distance formula of equation (1) to find the distance between plane ( x , 3 , z ) and ( x , y , z ) is calculated as follows: Distance between plane ( x , 3 , z ) and ( x , y , z ) = ( x − x ) 2 + ( y − 3 ) 2 + ( z − z ) 2 = ( 0 ) 2 + ( y − 3 ) 2 + ( 0 ) 2 = y 2 − 6 y + 9 { ∵ ( a − b ) 2 = a 2 − 2 a b + b 2 } Apply the distance formula of equation (1) to find the distance between plane ( x , − 1 , z ) and the point ( x , y , z ) is calculated as follows: Distance between plane ( x , − 1 , z ) and point ( x , y , z ) = ( x − x ) 2 + ( y − ( − 1 ) ) 2 + (

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 11.1, Problem 69E

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Calculate the equation for the set of all points equidistant from the planes y=3 and y=−1.

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Chapter 11.1, Problem 68E

Chapter 11.1, Problem 70E

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University Calculus: Early Transcendentals (4th Edition)

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