Solve the Problem $\mathrm { r } ^ { 2 } = \mathrm { k } \cos 2 \theta$

Multiple Choice

Solve the problem.
-Suppose that a radio signal transmission pattern can be modeled by $\mathrm { r } ^ { 2 } = \mathrm { k } \cos 2 \theta$ , for $0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }$ , where the units are in miles. Describe the influence of $k$ on the pattern. Assume that the positive $x$ -axis points east.

A) With increasing $k$ , the transmission becomes more strongly directed toward the north and less strongly directed to the east.
B) With increasing $\mathrm { k }$ , the distance of transmission becomes smaller in the east and west directions.
C) With increasing $k$ , the distance of transmission becomes greater in the east and west directions.
D) With increasing $\mathrm { k }$ , the transmission becomes more strongly directed toward the east and less strongly directed to the west.