A line is drawn through a fixed point (a,b) to meet the $X$-axis and $Y$-axis at $P$ and $Q$ respectively. Show that the minimum values of $PQ$, $OP+OQ$, and $OP\cdot OQ$ are respectively $(a^{2/3}+b^{2/3})^{3/2}$, $(\sqrt{a}+\sqrt{b})^2$, and $4ab$.
I set up the solution like this: $\frac{Q-b}{0-a}=\frac{b-0}{a-P}$. Is it correct?