\( P \) is a variable point on the ellipse \( \frac{x^{2}}{a^{2}}+\...

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\( P \) is a variable point on the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) with \( A A^{\prime} \) as the major axis. Then the maximum value of the area of the triangle \( A P A^{\prime} \) is
(A) \( a b \)
(B) \( 2 a b \)
\( \mathrm{P} \)
(C) \( a b / 2 \)
(D) None of these.
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