Answer to Question #160265 in Analytic Geometry for Priya

Question

Express the following surfaces in spherical coordinates.

i.xz=3

ii.x²+y²-z²=1

Answer 1

$\begin{cases} x=rsin\theta cos \psi ,\\ y=rsin\theta sin \psi ,\\ z=rcos\theta . \end{cases}$

1.

$r^2sin\theta cos \theta cos \psi=3.$

2.

$r^2cos2\theta=-1.$