Find an Equation in Spherical Coordinates for the Equation Given $$x ^ { 2 } + y ^ { 2 } - 4 z ^ { 2 } = 3$$

Multiple Choice

Find an equation in spherical coordinates for the equation given in rectangular coordinates. $$x ^ { 2 } + y ^ { 2 } - 4 z ^ { 2 } = 3$$

A)
$$\rho ^ { 2 } = \frac { 3 } { \left( \sin ^ { 2 } \phi - 4 \cos ^ { 2 } \phi \right) }$$
B)
$$\rho ^ { 2 } = \frac { 3 } { \left( \sin ^ { 2 } \theta - 4 \cos ^ { 2 } \theta \right) }$$
C)
$$\beta ^ { 2 } = \frac { 3 } { \left( \sin ^ { 2 } \phi - 4 \cos ^ { 2 } \theta \right) }$$
D)
$$\beta ^ { 2 } = \frac { 3 } { \left( \cos ^ { 2 } \phi - 4 \sin ^ { 2 } \phi \right) }$$
E)
$$\beta = - \sqrt { \frac { 3 } { 4 } }$$