Let a smooth curve \( v=f(x) \) be such that the slope of the tangent at any point \( (x, y) \) ...

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Let a smooth curve \( v=f(x) \) be such that the slope of the tangent at any point \( (x, y) \) on it is directly proportional to \( (-y / x) \). If the curve passes through the points \( (1,2) \) and \( (8,1) \), then \( \left|y\left(\frac{1}{8}\right)\right| \) is equal to
(a) \( 2 \log _{\mathrm{e}} 2 \)
(b) 4
(c) 1
(d) \( 4 \log _{\mathrm{e}} 2 \)
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