Example 1 Suppose the vertex of a parabola is at the origin $O$, $F$ is the focus, $PQ$ is a chord passing through $F$, $|OF|=a, |PQ|=$ $b$, find $S_{\triangle OPQ}$.
(1991 National High School League Question)
Solve $e=1, p=2|O F|=2 a, l=|P Q|=b$.
Let the equation of the chord $P Q$ be $y=k(x-a)$, i.e., $k x-y-a k=0$. By property 2, we know $k^{2}=\frac{e^{2} l}{l-2 e p}-1=$ $\frac{4 a}{b-4 a}$, the distance from point $O$ to $P Q$ is $h=\frac{a k}{\sqrt{1+k^{2}}}=\frac{2 a \sqrt{a}}{b}$, thus $S_{\triangle O P Q}=\frac{1}{2} b h=a \sqrt{a b}$.