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If the line \( a x+y=c \), touches both the curves \( x^{2}+y^{2}=1 \) and \( y^{2}=4 \sqrt{2} x \), then \( |c| \) is equal to
P
(a) \( \frac{1}{\sqrt{2}} \)
(b) 2
(c) \( \sqrt{2} \)
(2019 Main, 10 April, II)
W
(d) \( \frac{1}{2} \)
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