Question: Find Orthogonal trajectories to the family of straight lines y=k(x-1) where k in RSolution : Given family of straight lines \[y=k(x-1) \] (1) To obtain Orthogonal trajectories Step 1:Differentiating with respect to x \[\frac{dy}{dx}=k\] Step 2: replace \[\frac{dy}{dx} \]…