The directrix of parabola $C : y ^ { 2 } = 4 x$ is $l$. Let $P$ be a moving point on $C$. Draw a tangent line to circle $\odot A : x ^ { 2 } + ( y - 4 ) ^ { 2 } = 1$ through $P$, with $Q$ as the point of tangency. Draw a perpendicular from $P$ to line $l$, with $B$ as the foot of the perpendicular. Then A. Line $l$ is tangent to $\odot A$ B. When $P , A , B$ are collinear, $| P Q | = \sqrt { 15 }$ C. When $| P B | = 2$, $P A \perp A B$ D. There are exactly 2 points $P$ satisfying $| P A | = | P B |$
The directrix of parabola $C : y ^ { 2 } = 4 x$ is $l$. Let $P$ be a moving point on $C$. Draw a tangent line to circle $\odot A : x ^ { 2 } + ( y - 4 ) ^ { 2 } = 1$ through $P$, with $Q$ as the point of tangency. Draw a perpendicular from $P$ to line $l$, with $B$ as the foot of the perpendicular. Then\\
A. Line $l$ is tangent to $\odot A$\\
B. When $P , A , B$ are collinear, $| P Q | = \sqrt { 15 }$\\
C. When $| P B | = 2$, $P A \perp A B$\\
D. There are exactly 2 points $P$ satisfying $| P A | = | P B |$