Find the orthogonal trajectories of the family of curves.

Question

Quizplus · Accepted Answer

To find the orthogonal trajectories, we need to find the family of curves orthogonal to the given family, which is given by $\frac{dy}{dx}=\frac{-x}{y}$. Taking the negative reciprocal, we get $\frac{dy}{dx}=\frac{y}{x}$. This is the differential equation satisfied by the orthogonal trajectories.

Solving this differential equation, we get $y=cx$, where $c$ is a constant. Therefore, the family of orthogonal trajectories is given by $y=cx$, where $c$ is a constant.

Thus, the correct answer is (A).

Find the Orthogonal Trajectories of the Family of Curves