Thread: Orthogonal Trajectories

I'm confused as to how to do orthogonal trajectory problems. The current calculus book I have doesn't explain how to do these problems, yet these problems appear in the back of some of the chapters in the book.

Here's an example problem:

Find the value of the number a such that the families of curves and are orthogonal trajectories.

How would I go about doing this?

Orthogonal trajectories are families of curves that intersect at right angles. This must mean that the product of their respective derivatives is -1.

Let's see what you get.

Originally Posted by TKHunny

Orthogonal trajectories are families of curves that intersect at right angles. This must mean that the product of their respective derivatives is -1.

Let's see what you get.

I think it must be "...the product of their respective derivatives at their intersection point is -1"

Tonio

One related question:
Since they're orthogonal then it means that y' of the first is (m) and y' of the other is (-1/m) at their point of intersection right?

Well, for m NOT = zero (0), m*(-1/m) = -1