Question

Transform to Cartesian coordinates the equation:

$r=\alpha 2\sin \theta$

Answer 1

Given equation is

$r=\alpha 2\sin \theta$ ....... $\left(i\right)$

We know that,

$x=r\cos \theta$

$y=r\sin \theta$

$\Rightarrow r=\alpha 2\times \frac{y}{r}$ ...... From $\left(i\right)$

$\Rightarrow r^2=2\alpha \times y$

Using result $r=\sqrt{x^2+y^2}$ in above equation

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