Let $P$ be the point on the parabola $y^2=4 x$ which is at the shortest distance from the centre $S$ of the circle $x^2+y^2-4 x-16 y+64=0$. Let $Q$ be the point on the circle dividing the lie segment SP internally. Then
Select ALL correct options:
A
$S P=2 \sqrt{5}$
B
$\mathrm{SQ}: \mathrm{QP}=(\sqrt{5}+1): 2$
C
the $x$-intercept of the normal to the parabola at $P$ is 6
D
the slope of the tangnet to the circle at $Q$ is $\frac{1}{2}$
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