A circle touches the parabola \( y^{2}=4 x \) at the point \( (1 \), \( 2) \) and also the direc....

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A circle touches the parabola \( y^{2}=4 x \) at the point \( (1 \), \( 2) \) and also the directrix. The \( y \)-coordinate of the point of contact of the circle and the directrix is
\( \mathrm{P} \)
(1) \( \sqrt{2} \)
(2) 2
(3) \( 2 \sqrt{2} \)
(4) 4


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