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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Describe the traces of the surface given by x 2 + y 2   z 2 =   1 in the xy-plane, the yz-plane, the xz-plane, and the plane given by z = 3. Then classify the surface.

To determine

To graph: The trace of the surface x2+y2z2=1 in x-y plane, the x-z plane, the y-z plane and the plane given by z=3 and also classify the surfaces.

Explanation

Given information:

The equation is x2+y2z2=1.

Graph:

Consider equation of plane,

x2+y2z2=1 ...... (1)

Substitute, 0 for z in equation (1) for xy-plane,

x2+y2z2=1x2+y202=1x2+y2=1

Hence, x2+y2=1 is equation of circle. This can be drawn by MAPLE by executing the below code,

with(plots)

a := implicitplot3d(x^2+y^2-z^2 = 1, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, color = red, transparency = .5, style = surface, axes = normal);

b := implicitplot3d(z = 0, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5,

color = grey, transparency = 0.5, style = surface)

display(a, b);

Output:

Now substitute 0 for x in equation (1) for yz-plane,

02+y2z2=1y2z2=1

Hence, y2z2=1 is equation of Hyperbola. This can be drawn by MAPLE by executing the below code,

with(plots)

a := implicitplot3d(x^2+y^2-z^2 = 1, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, color = red, transparency = .5, style = surface, axes = normal);

b := implicitplot3d(x = 0, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5,

color = grey, transparency = 0.5, style = surface)

display(a, b);

Output:

Now substitute, 0 for y in equation (1) for xz-plane

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