MathNet 2009-part-01 — 175 problems (EN–VI) Question 122

Given points $P$, $Q$ on an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a \gt b \gt 0$), satisfying $OP \perp OQ$, the minimum of $|OP| \times |OQ|$ is ____.