# Orthogonal Trajectories

• June 2nd 2008, 10:14 AM
Jessica098
Orthogonal Trajectories
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.

• June 2nd 2008, 06:18 PM
mr fantastic
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.

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 $\frac{dy}{dx} = \frac{2y}{x}$ .......