A line \( a x+b y+c=0 \) through the point \( A(-2,0) \) \( \mathrm...

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A line \( a x+b y+c=0 \) through the point \( A(-2,0) \)
\( \mathrm{P} \) intersects the curve \( y^{2}=4 x \) in \( P \) and \( Q \) such that

W \( \frac{1}{A P}+\frac{1}{A Q}=\frac{1}{4}(P, Q \) are in 1 st quadrant \( ) \). The value of \( \sqrt{a^{2}+b^{2}+c^{2}} \) is:
(1) 2
(2) 4
(3) 6
(4) 8
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