Find the Orthogonal Trajectories of the Family of Curves $$y = k x ^ { 9 }$$

Multiple Choice

Find the orthogonal trajectories of the family of curves.
$$y = k x ^ { 9 }$$

A) $x ^ { 2 } - 8 y ^ { 2 } = 0$
B) $x ^ { 2 } - 8 y ^ { 2 } = C$
C) $x ^ { 2 } - y ^ { 2 } = 0$
D) $x ^ { 2 } + 8 y ^ { 2 } = 0$
E) $x ^ { 2 } + 9 y ^ { 2 } = C$