# Math Help - Orthogonal Trajectories

1. ## 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 $y=(x+c)^{-1}$ and $y=a(x+k)^{1/3}$ are orthogonal trajectories.

How would I go about doing this?

2. 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.

3. 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

4. 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?

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