Name:

1.  What's does the following equation represent \(36x^2 + 9 y^2 + 4z^2 = 36\)?

a.  A sphere of radius 6 centered at the origin.

b.  An elipsoid centered at the origin, crossing the x-axis at 1 and -1.

c.  An elipsoid centered at the origin, crossing the x-axis at 6 and -6.

d.  A hyperboloid of one sheet.

e.  A hyperboloid of two sheets.

2.  What's does the following equation represent \(36x^2 - 9 y^2 + 4z^2 = 36\)?

a.  A sphere of radius 6 centered at the origin.

b.  An elipsoid centered at the origin, crossing the x-axis at 1 and -1.

c.  An elipsoid centered at the origin, crossing the x-axis at 6 and -6.

d.  A hyperboloid of one sheet.

e.  A hyperboloid of two sheets.

3.  What's does the following equation represent \(36x^2 - 9 y^2 + 4z^2 = -36\)?

a.  A sphere of radius 6 centered at the origin.

b.  An elipsoid centered at the origin, crossing the x-axis at 1 and -1.

c.  An elipsoid centered at the origin, crossing the x-axis at 6 and -6.

d.  A hyperboloid of one sheet.

e.  A hyperboloid of two sheets.

4.  What's does the following equation represent \(x + y^2 + z^2 = 0\)?

a.  A paraboloid opening on the positive z-axis.

b.  A paraboloid opening on the negative z-axis.

c.  A paraboloid opening on the positive x-axis.

d.  A paraboloid opening on the negative x-axis.

e.  A paraboloid opening on the positive y-axis.

5.  What's does the following equation represent \(r = z\)? (You're meant to infer the coordinate system we're using here.)

a.  Two straight lines in the rz-plane.

b.  A paraboloid opening on the positive z-axis.

c.  A paraboloid opening on the positive x-axis.

d.  A cone centered around the z-axis.

e.  A cone centered around the r-axis.

6.  What's does the following equation represent \(r^2 + z^2 = 1\)?

a.  A sphere of radius 1.

b.  Just the point at the origin.

c.  A paraboloid opening on the positive x-axis.

d.  A hyperboloid of two sheets opening on the z-axis.

e.  A parabolic hyerboloid.

7.  What's does the following set of equations represent \(\rho \leq 1, 0 \leq \theta \leq \frac{\pi}{2}, 0\leq \phi \leq \frac{\pi}{2})?

a.  A solid sphere of radius 1.

b.  Half of a solid sphere of radius 1.

c.  One third of a solid sphere of radius 1.

d.  One quarter of a solid sphere of radius 1.

e.  One eighth of a solid sphere of radius 1.