Final answer:
To find the orthogonal trajectories of the family of curves, differentiate the given equations with respect to x, take the reciprocal, and solve the resulting differential equations.
Step-by-step explanation:
The orthogonal trajectories of the family of curves can be found by determining the differential equation representing this family of curves, and then solving it. The given equations are as follows:
a) y = -1/(13kx)
b) y = -x/(13k)
c) y = 13kx
d) y = x/13k
To find the orthogonal trajectories, we differentiate the given equations with respect to x, and then multiply the resulting equations by -1 and take the reciprocal.
After solving the differential equations, we can use a graphing device to draw several members of each family on a common screen to visualize the orthogonal trajectories.