Kepler’s second law is a consequence of:

$\frac{dA}{dt}$ = constant

$\Rightarrow \frac{d}{dt}\left(\frac{1}{2} r^2 \theta\right)$ = k

$\Rightarrow \frac{r^2}{2}\left(\frac{d \theta}{dt}\right)$ = k

$\Rightarrow r^2 \omega = 2 k$

$\Rightarrow mr^2 \omega$ = 2 mk

⇒ L = 2 mk = constant ; L = angular momentum