The area of the smaller region enclosed by the curves \( y^{2}=8 x+4 \) and \( x^{2}+y^{2}+4 \sq...

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The area of the smaller region enclosed by the curves \( y^{2}=8 x+4 \) and \( x^{2}+y^{2}+4 \sqrt{3} x-4=0 \) is equal to
(a) \( \frac{1}{3}(2-12 \sqrt{3}+8 \pi) \)
(b) \( \frac{1}{3}(2-12 \sqrt{3}+6 \pi) \)
(c) \( \frac{1}{3}(4-12 \sqrt{3}+8 \pi) \)
(d) \( \frac{1}{3}(4-12 \sqrt{3}+6 \pi) \)
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