Consider a region $R = \left\{ ( x , y ) \in R ^ { 2 } : x ^ { 2 } \leq y \leq 2 x \right\}$. If a line $y = \alpha$ divides the area of region $R$ into two equal parts, then which of the following is true?\\
(1) $\alpha ^ { 3 } - 6 \alpha ^ { 2 } + 16 = 0$\\
(2) $3 \alpha ^ { 2 } - 8 \alpha ^ { 3 / 2 } + 8 = 0$\\
(3) $3 \alpha ^ { 2 } - 8 \alpha + 8 = 0$\\
(4) $\alpha ^ { 3 } - 6 \alpha ^ { 3/2 } + 16 = 0$