2. The line $\frac{x}{4}+\frac{y}{3}=1$ intersects the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$ at points $A$ and $B$. A point $P$ on the ellipse makes the area of $\triangle P A B$ equal to 3. How many such points $P$ are there?
A. 1
B. 2
C. 3
D. 4
2. B Let point $Q(4 \cos t, 3 \sin t)$ be on the "minor arc" opposite to line $A B$. It is known that the area of triangle $A B Q$ is $6 \sin t + 6 \cos t - 6 = 6 \sqrt{2} \sin \left(t + \frac{\pi}{4}\right) - 6 \leqslant 6 \sqrt{2} - 6 < 3$, which means point $P$ has 2 solutions.