The tangent at a point \( P \) on the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) ...

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The tangent at a point \( P \) on the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) passes through the point \( (0,-b) \) and the normal at \( P \) passes through the point \( (2 a \sqrt{2}, 0) \). Then the eccentricity of the hyperbola is
(A) 2
(B) \( \sqrt{2} \)
(C) 3
(D) \( \sqrt{3} \)
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