Opposite Slopes and a Fixed Chord Slope

Let $A(2,1)$ be a fixed point on the hyperbola $\dfrac{x^2}2-y^2=1$, and let $P,Q$ be two points on the hyperbola such that the slopes of $AP$ and $AQ$ are negatives of each other.

1. Find the slope of the line $PQ$. 2. If $\tan\angle PAQ=2\sqrt 2$, find the area of $\triangle PAQ$.