Let \( P(x, y) \) be a variable point such that
\( \mathrm{P} \)
\[
\left|\sqrt{(x-1)^{2}+(y-2)^{2}}-\sqrt{(x-5)^{2}+(y-5)^{2}}\right|=3
\]
W
which represents a hyperbola.
If the origin is shifted to the point \( (3,7 / 2) \) and the axes are rotated through an angle \( \theta \) in clockwise sense so that the equation of the given hyperbola changes to the standard form \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \), then \( \theta \) is
(1) \( \tan ^{-1}(4 / 3) \)
(2) \( \tan ^{-1}(3 / 4) \)
(3) \( \tan ^{-1}(5 / 3) \)
(4) \( \tan ^{-1}(3 / 5) \)
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