Parallel Beams of Similarly Charged Particles Are Shot from Two $L = 24$

Parallel beams of similarly charged particles are shot from two atomic accelerators $L = 24$ meters apart, as shown in the figure below. If the particles were not deflected, the beams would be $H = 2.4 \times 10 ^ { - 4 }$ meters apart. However, because the charged particles repel each other, the beams follow the hyperbolic path $y = \frac { k } { x }$ , for some $k$ . Find $k$ .

A) $\quad k = 2.88 \times 10 ^ { - 3 }$
B) $\quad k = 1.44 \times 10 ^ { - 3 }$
C) $\quad k = 1.44$
D) $\quad k = 1.44 \times 10 ^ { - 6 }$
E) none of these