The tangent at a point \( P \) on the hyperbola \( \mathrm{P}^{16: ...

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The tangent at a point \( P \) on the hyperbola
\( \mathrm{P}^{16: 4} \) \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) meets one of the directrix at \( F \). If \( P F \)

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subtends an angle \( \theta \) at the corresponding focus, then
\( \theta= \)
(1) \( \pi / 4 \)
(2) \( \pi / 2 \)
(3) \( 3 \pi / 4 \)
(4) \( \pi \)
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