Find an Equation in Rectangular Coordinates for the Equation Given $r ^ { 2 } + z ^ { 2 } = 4$

Multiple Choice

Find an equation in rectangular coordinates for the equation given in cylindrical coordinates. $r ^ { 2 } + z ^ { 2 } = 4$

A) $x + y + z = 2$
B) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$
C) $x ^ { 2 } + y ^ { 2 } + \left( \frac { z } { 2 } \right) ^ { 2 } = 0$
D) $x ^ { 2 } + y ^ { 2 } = - 4 z ^ { 2 }$
E) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 2$