Tangent polar graphs

Question

For what values of $k$ is the relationship $r=k\sec\theta$ tangent to the relationship $r=-4\cos\theta$?

Since $r=-4\cos\theta$ is basically a circle with radius $2$ and center $(-2,0)$, and $r=k\sec\theta$ is equal to $x=k$, shouldn't $k$ be $-4$ and $0$? Why does the answer seem to emphasise that it is $x=-4$ only?

Answer 1

If $k=0$ the first locus becomes $r=0$ which is a single point so cannot be tangent to the circle