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: $\displaystyle 2x + 4y \, \frac{dy}{dx} = 0 \Rightarrow \frac{dy}{dx} = - \frac{x}{2y}$.
So the orthogonal trajectories are the family of curves given by the solutions to the differential equation $\displaystyle \frac{dy}{dx} = \frac{2y}{x}$ .......