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Multivariable Calculus

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Difficult

Find the True Statement

MVCALC-PSJHJA

Let $S$ be a surface whose equation in spherical coordinates is:

$$\sin^2 \phi=\rho^2$$

Which of the following statements is TRUE?

A

The plane $z=1.1$ intersects $S$

B

The intersection of $S$ with the plane $z=0$ is only a circle.

C

The plane $z=-2$ intersects $S$

D

The intersection of $S$ with the plane $z=0$ is a circle and the origin.

E

The only point on $S$ whose three rectangular coordinates are all the same is the origin.