The area (in sq units) of the smaller of the two circles that touch the parabola, \( y^{2}=4 x \...

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The area (in sq units) of the smaller of the two circles that touch the parabola, \( y^{2}=4 x \) at the point \( (1,2) \) and the \( X \)-axis is
(2019 Main, 9 April, II)
(a) \( 8 \pi(3-2 \sqrt{2}) \)
(b) \( 4 \pi(3+\sqrt{2}) \)
(c) \( 8 \pi(2-\sqrt{2}) \)
(d) \( 4 \pi(2-\sqrt{2}) \)
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