Hi! I am currently working on some calc2 online homework problems and I am having difficulty with this problem. I was trying to use the polar coordinates (d,a)with the equation of the line thus being r=dsec(theta-a). I tried solving for d by setting d equal to sqrt((-19)^2+(-6)^2) which then came out to be 137621/6907. I then tried solving for a by setting it equal to arctan(-6/-19) which came out to be 17.52556837. I then plugged everything into the equation of the line which i had as r=dsec(theta-a) to get r= (137621/6907)sec(theta-17.52556837). Clearly my answer is wrong but I do not know why. If someone can help me solve this problem I would greatly appreciate it.
The line is
$$L:\;\; y=-\frac{19}6x-\frac{208}3$$
and passing to polar coordinates:
$$r\sin\theta=-\frac{19}6r\cos\theta-\frac{208}3\implies r=-\frac{416}{6\sin\theta+19\cos\theta}$$