Question

Transform to Cartesian coordinates the equation:

$r=\alpha \cos \theta$

Answer 1

Given equation is

$r=\alpha \cos \theta$ ...... $\left(i\right)$

$x=r\cos \theta$

$y=r\sin \theta$

Using above result in $\left(i\right)$

$\Rightarrow r=\alpha \times \frac{x}{r}$

$\Rightarrow r^2=\alpha x$

$\Rightarrow x^2+y^2=\alpha x$