Consider the curve \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\). The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of
(A) \(\frac{\pi}{4}\)
(B) \(\frac{\pi}{3}\)
(C) \(\frac{\pi}{2}\)
(D) \(\frac{\pi}{6}\)
