Let $t$ be TNYWR.

If the graph of $y=2 \sqrt{2 t} \sqrt{x}-2 t$ passes through the point $(a, a)$, what is the value of $a$ ?
Since the graph of $y=2 \sqrt{2 t} \sqrt{x}-2 t$ passes through the point ( $a$, a), then $a=2 \sqrt{2 t} \sqrt{a}-2 t$. Rearranging, we obtain $a-2 \sqrt{2 t} \sqrt{a}+2 t=0$. We re-write as $(\sqrt{a})^{2}-2 \sqrt{a} \sqrt{2 t}+(\sqrt{2 t})^{2}=0$ or $(\sqrt{a}-\sqrt{2 t})^{2}=0$.

Therefore, $\sqrt{a}=\sqrt{2 t}$ or $a=2 t$.

Since the answer to (a) is 3 , then $t=3$ and so $a=6$.