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Let \( a, b, c \) be three vectors such that each of them are non-collinear, \( \mathbf{a}+\mathbf{b} \) and \( \mathbf{b}+\mathbf{c} \) are collinear with \( \mathbf{c} \) and \( \mathbf{a} \)
\( \mathrm{P} \) respectively and \( \mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{k} \). Then, \( (|\mathbf{k}|,|\mathbf{k}|) \) lies on

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(a) \( y^{2}=4 a x \)
(b) \( x^{2}+y^{2}-a x-b y=0 \)
(c) \( x^{2}-y^{2}=1 \)
(d) \( |x|+|y|=1 \)
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