- #1

Westlife

- 4

- 2

## Homework Statement

Find Orthogonal Trajectories of ##\frac{x^2}{a}-\frac{y^2}{a-1}=1##

Hint

Substitute a new independent variable w

##x^2=w##

and an new dependent variable z

##y^2=z##

## Homework Equations

## The Attempt at a Solution

substituting ##x## and ##y## I get

$$\frac{w}{a}-\frac{z}{a-1}=1\quad /a(a-1)$$

$$w(a-1)-za=a(a-1)\quad /'$$

$$w'(a-1)-z'a=0$$

Here I wanted to figure out what ##w'##and ##z'## are and here is where I get confused. How do I get them?

since w is now the new independent variable is ##w'= \frac{dw}{dw}=1## and ##z'=\frac{dz}{dw}## or does mean mean something else ?