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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

A surface consists of all points P such that the distance from P to the plane y = 1 is twice the distance from P to the point (0, −1, 0). Find an equation for this surface and identify it.

To determine

To find and identify: An equation of the surface.

Explanation

Given data:

Distance P to the point (0,1,0) and plane is y=1 .

Formula used:

Consider the standard equation of an ellipsoid.

x2a2+y2b2+z2c2=1 (1)

Consider point P(x,y,z) .

The distance from (D) P(x,y,z) to (0,1,0) .

D=(x0)2+(y+1)2+(z0)2D=(x)2+(y+1)2+(z)2

As the plane y=1 is twice the distance from P(x,y,z) to the point (0,1,0) that is,

|y1|=2D

Substitute (x)2+(y+1)2+(z)2 for D ,

|y1|=2((x)2+(y+1)2+(z)2)(y1)2=4[(x)2+(y+1)2+(z)2](y1)2=4(x)2+4(y+1)2+4(z)2y22y+1=4x2+4(y2+2y+1)+4z2

Rearrange the equation

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Chapter 12 Solutions

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Sect-12.1 P-11ESect-12.1 P-12ESect-12.1 P-13ESect-12.1 P-14ESect-12.1 P-15ESect-12.1 P-16ESect-12.1 P-17ESect-12.1 P-18ESect-12.1 P-19ESect-12.1 P-20ESect-12.1 P-21ESect-12.1 P-22ESect-12.1 P-23ESect-12.1 P-24ESect-12.1 P-25ESect-12.1 P-26ESect-12.1 P-27ESect-12.1 P-28ESect-12.1 P-29ESect-12.1 P-30ESect-12.1 P-31ESect-12.1 P-32ESect-12.1 P-33ESect-12.1 P-34ESect-12.1 P-35ESect-12.1 P-36ESect-12.1 P-37ESect-12.1 P-38ESect-12.1 P-39ESect-12.1 P-40ESect-12.1 P-41ESect-12.1 P-42ESect-12.1 P-43ESect-12.1 P-44ESect-12.1 P-45ESect-12.1 P-46ESect-12.1 P-47ESect-12.1 P-48ESect-12.2 P-1ESect-12.2 P-2ESect-12.2 P-3ESect-12.2 P-4ESect-12.2 P-5ESect-12.2 P-6ESect-12.2 P-7ESect-12.2 P-8ESect-12.2 P-9ESect-12.2 P-10ESect-12.2 P-11ESect-12.2 P-12ESect-12.2 P-13ESect-12.2 P-14ESect-12.2 P-15ESect-12.2 P-16ESect-12.2 P-17ESect-12.2 P-18ESect-12.2 P-19ESect-12.2 P-20ESect-12.2 P-21ESect-12.2 P-22ESect-12.2 P-23ESect-12.2 P-24ESect-12.2 P-25ESect-12.2 P-26ESect-12.2 P-27ESect-12.2 P-28ESect-12.2 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P-48ESect-12.6 P-49ESect-12.6 P-50ESect-12.6 P-51ESect-12.6 P-52ECh-12 P-1RCCCh-12 P-2RCCCh-12 P-3RCCCh-12 P-4RCCCh-12 P-5RCCCh-12 P-6RCCCh-12 P-7RCCCh-12 P-8RCCCh-12 P-9RCCCh-12 P-10RCCCh-12 P-11RCCCh-12 P-12RCCCh-12 P-13RCCCh-12 P-14RCCCh-12 P-15RCCCh-12 P-16RCCCh-12 P-17RCCCh-12 P-18RCCCh-12 P-19RCCCh-12 P-1RQCh-12 P-2RQCh-12 P-3RQCh-12 P-4RQCh-12 P-5RQCh-12 P-6RQCh-12 P-7RQCh-12 P-8RQCh-12 P-9RQCh-12 P-10RQCh-12 P-11RQCh-12 P-12RQCh-12 P-13RQCh-12 P-14RQCh-12 P-15RQCh-12 P-16RQCh-12 P-17RQCh-12 P-18RQCh-12 P-19RQCh-12 P-20RQCh-12 P-21RQCh-12 P-22RQCh-12 P-1RECh-12 P-2RECh-12 P-3RECh-12 P-4RECh-12 P-5RECh-12 P-6RECh-12 P-7RECh-12 P-8RECh-12 P-9RECh-12 P-10RECh-12 P-11RECh-12 P-12RECh-12 P-13RECh-12 P-14RECh-12 P-15RECh-12 P-16RECh-12 P-17RECh-12 P-18RECh-12 P-19RECh-12 P-20RECh-12 P-21RECh-12 P-22RECh-12 P-23RECh-12 P-24RECh-12 P-25RECh-12 P-26RECh-12 P-27RECh-12 P-28RECh-12 P-29RECh-12 P-30RECh-12 P-31RECh-12 P-32RECh-12 P-33RECh-12 P-34RECh-12 P-35RECh-12 P-36RECh-12 P-37RECh-12 P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

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