To determine Calculate the equation for the set of points equidistant from the y -axis and the plane z = 6 . Explanation Given information: The y -axis. The plane z = 6 . 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 y -axis is ( 0 , y , 0 ) and the point representation for the plane is ( x , y , 6 ) . Apply the distance formula of equation (1) to find the distance between y -axis ( 0 , y , 0 ) and the point ( x , y , z ) is calculated as follows: Distance between y -axis ( 0 , y , 0 ) and point ( x , y , z ) = ( x − 0 ) 2 + ( y − y ) 2 + ( z − 0 ) 2 = ( x ) 2 + ( 0 ) 2 + ( z ) 2 = x 2 + z 2 Apply the distance formula of equation (1) to find the distance between plane ( x , y , 6 ) and the point ( x , y , z ) is calculated as follows: Distance between plane ( x , y , 6 ) and point ( x , y , z ) = ( x − x ) 2 + ( y − y ) 2 + ( z − 6 ) 2 = ( 0 ) 2 + ( 0 ) 2 + ( z 2 − 12 z + 36 ) { ∵ ( a − b ) 2 = a 2 − 2 a b + b 2 } = z 2 − 12 z + 36 The equation for the set of all points equidistant from the planes y = 3 and y = − 1 is calculated as follows

Thomas' Calculus - MyMathLab Integrated Review

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ISBN: 9780134786223

Author: Hass

Publisher: PEARSON

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Chapter 12.1, Problem 74E

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Calculate the equation for the set of points equidistant from the y-axis and the plane z=6.

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Chapter 12.1, Problem 73E

Chapter 12.1, Problem 75E

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