Given the polar curve $~r=1+2\cos\theta~$ for $~\theta \in \left[ 0,2\pi \right)\,$, determine which of the following lines are tangent to the curve at the pole (the origin).
Line equation|Yes or No
:-:|:-:
$y=-x$|[[☃ dropdown 6]]
$y=-\sqrt3\,x$|[[☃ dropdown 7]]
$y=\sqrt3\,x$|[[☃ dropdown 8]]
$y=x$|[[☃ dropdown 9]]
$x=0$|[[☃ dropdown 10]]