- #1

patric44

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- Homework Statement
- in the polar coordinates find the set of curves that intersects with a right angle with the set of curves describes by r^{2} = a^{2}cos(theta)

- Relevant Equations
- r^{2} = a^{2}cos(θ)

there is a problem in a book that asks to find the orthogonal trajectories to the curves described by the equation :

$$r^{2} = a^{2}\cos(\theta)$$

the attempt of a solution is as following :

1- i defferntiate with respect to ##\theta## :

$$2r \frac{dr}{d\theta} = -a^{2}\;\sin(\theta)$$

2- i eliminated "a" from the two equations and get :

$$\frac{dr}{d\theta} = -\frac{1}{2}tan(\theta)$$

then the book said to set ##\frac{dr}{d\theta} = -r^{2}\frac{d\theta}{dr} ## ! , this step i don't get ? why would i do that , it doesn't seem to be equal ?!

$$r^{2} = a^{2}\cos(\theta)$$

the attempt of a solution is as following :

1- i defferntiate with respect to ##\theta## :

$$2r \frac{dr}{d\theta} = -a^{2}\;\sin(\theta)$$

2- i eliminated "a" from the two equations and get :

$$\frac{dr}{d\theta} = -\frac{1}{2}tan(\theta)$$

then the book said to set ##\frac{dr}{d\theta} = -r^{2}\frac{d\theta}{dr} ## ! , this step i don't get ? why would i do that , it doesn't seem to be equal ?!