Answer:
A. Circular Cylinder
r=4
[tex]\sqrt{x^{2}+y^{2} }[/tex] =4 independent from z
B. Plane
ρ cos
φ ( )=4
spherical coordinates
z=4
C. Cone
φ =
π/3
φ spherical coordinates
D. Half Plane
θ
=
π/3
Cylindrical Coordinates, do not have portion in 3rd quadrant that why its only half a plane.
E. Sphere:
ρ
=2cos φ ( )
Spherical Coordinates
ρ
=2×z/ρ
[tex]p^{2}[/tex] =2z
[tex]x^{2} +y^{2} +z^{2}[/tex] =
[tex]p^{2}[/tex]
[tex]x^{2} +y^{2}+z-1^{2}[/tex]=1
F. Elliptic or Circular Parabola
z=[tex]r^{2}[/tex]
z=[tex]r^{2}[/tex] = [tex]x^{2} +y^{2}[/tex]
z= [tex]y^{2}[/tex]
note: pics are attached
