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12 Nov 2019

1. Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is 3 times the distance from P to the yz-plane.


2. Identify the surface.

hyperboloid of two sheets

elliptic paraboloid

ellipsoid

hyperbolic paraboloid

elliptic cylinder

parabolic cylinder

cone

hyperboloid of one sheet

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Casey Durgan
Casey DurganLv2
5 Jun 2019

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Related questions

(a) Find and identify the traces of the quadric surface

x2 + y2 ? z2 = 16

given the plane.

x = k

Find the trace.


Identify the trace.

circle

ellipse

hyperbola

parabola

y = k

Find the trace.


Identify the trace.

circle

ellipse

hyperbola

parabola

z = k

Find the trace.


Identify the trace.

circle

ellipse

hyperbola

parabola


Describe the surface from one of the graphs in the table.

ellipsoid

elliptic paraboloid hyperbolic paraboloid

cone

hyperboloid of one sheet

hyperboloid of two sheets


(b) If we change the equation in part (a) to

x2 ? y2 + z2 = 16,

how is the graph affected?

The graph is rotated so that its axis is the x-axis.The graph is rotated so that its axis is the y-axis. The graph is rotated so that its axis is the z-axisThe graph is shifted one unit in the negative y-direction.The graph is shifted one unit in the positive y-direction.



(c) What if we change the equation in part (a) to

x2 + y2 + 2y ? z2 = 15?

The graph is rotated so that its axis is the x-axis.The graph is rotated so that its axis is the y-axis. The graph is rotated so that its axis is the z-axisThe graph is shifted one unit in the negative y-direction.The graph is shifted one unit in the positive y-direction.

1. Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is 3 times the distance from P to the yz-plane.

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