Orthogonal Trajectories

Quote:

Originally Posted by Jessica098

I need some quick homework help with a calculus problem. The problem is as follows:

Find the orthogonal trajectories of the family of curves:

(x^2)+(2y^2)=18k^2 where k is any real number.

Help please!!!!

I assume you know the definition of an orthogonal trajectory.

Using implicit differentiation: $2x + 4y \, \frac{dy}{dx} = 0 \Rightarrow \frac{dy}{dx} = - \frac{x}{2y}$ .

So the orthogonal trajectories are the family of curves given by the solutions to the differential equation $\frac{dy}{dx} = \frac{2y}{x}$ .......