Question

Match the given equation with the verbal description of the surface: A. Circular Cylinder B. Plane C. Cone D. Half plane E. Sphere F. Elliptic or Circular Paraboloid

Answer 1

Answer:

A. Circular Cylinder  

            r=4                                  

     $\sqrt{x^{2}+y^{2} }$ =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

$p^{2}$ =2z

$x^{2} +y^{2} +z^{2}$ = $p^{2}$  

$x^{2} +y^{2}+z-1^{2}$=1

F. Elliptic or Circular Parabola

z=$r^{2}$                                    

z=$r^{2}$ = $x^{2} +y^{2}$                                      

z= $y^{2}$

note: pics are attached