   Chapter 12.6, Problem 48E

Chapter
Section
Textbook Problem

# Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is twice the distance from P to the yz-plane. Identify the surface.

To determine

To find: An equation for the surface.

Explanation

Formula used:

Consider the two points as (x1,y1,z1) and (x2,y2,z2) .

d=(x1x2)2+(y1y2)2+(z1z2)2 (1)

Consider the general surface equation of circular cone along the x-axis.

x2a2=y2b2+z2c2 (2)

Consider the point P as (x,y,z) .

Consider the point along the x-axis is (x,0,0) and the point on the yz-plane is (0,y,z) .

Find the distance from point P (x,y,z) to x-axis (x,0,0) using equation (1).

d1=(xx)2+(y0)2+(z0)2=02+y2+z2=y2+z2

Find the distance from point P (x,y,z) to point on the yz-plane (0,y,z) using equation (1)

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