A line passing through the point \( (3,4) \) and making an angle \(...

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A line passing through the point \( (3,4) \) and making an angle \( \theta \) with the positive direction of \( x \)-axis, intersects the line \( x+y=8 \) at a distance \( \frac{1}{3} \sqrt{6} \) units from the point, then \( \theta \) is equal to
(a) \( -\frac{\pi}{12} \)
(b) \( \frac{\pi}{12} \)
(c) \( \frac{5 \pi}{12} \)
(d) \( \frac{7 \pi}{12} \)
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