question_answer

Let P be the point on the parabola \[{{y}^{2}}=4x\] which is at the shortest distance from the center S of the circle \[{{x}^{2}}+{{y}^{2}}-4x-16y+64=0\]. Let Q be the point on the circle dividing the line segment SP internally. Then

A)  \[SP=2\sqrt{5}\]

B)  \[SQ:QP=(\sqrt{5}+1):4\]

C)  The slope of the tangent to the circle at Q is \[\frac{1}{2}\]

D)  All of these

E)  None of these