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Let P be the point on the parabola y^(2)...

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=2sqrt(5)`

B

`SQ : QP= (sqrt(5)+1): 2`

C

the x-intercept of the normal to the parabola at P is 6

D

the slope of the tangent to the circle at Q is `(1)/(2)`

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A, C, D
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