Let \( A \equiv(-3,4) \) and \( B \equiv(2,-1) \) be two fixed points. A point \( C \) moves suc...

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Let \( A \equiv(-3,4) \) and \( B \equiv(2,-1) \) be two fixed points.
A point \( C \) moves such that
\( \mathrm{P} \)
\[
\tan \left(\frac{1}{2} \angle A B C\right): \tan \left(\frac{1}{2} \angle B A C\right)=3: 1
\]
W
Thus, locus of \( C \) is a hyperbola, distance between whose foci is
(a) 5
(b) \( 5 \sqrt{2} \)
(c) \( \frac{5}{2} \)
(d) \( \frac{5}{\sqrt{2}} \)
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