第 034 题 / 73

三支不同的曲线 $y = {a}_{i} \cdot \left| {x - 1}\right| \left( {{a}_{i} > 0,i = 1,2,3}\right)$ 交抛物线 ${y}^{2} = {4x}$ 于点 ${A}_{i},{B}_{i}\left( {i = 1,2,3}\right) ,F$ 为抛物线的焦点，记 $\bigtriangleup {A}_{i}F{B}_{i}$ 的面积为 ${S}_{i}$ ，下列说法正确的是（ ）
A. $\frac{1}{\left| F{A}_{i}\right| } + \frac{1}{\left| F{B}_{i}\right| }\left( {i = 1,2,3}\right)$ 为定值
B. ${A}_{1}{B}_{1}//{A}_{2}{B}_{2}//{A}_{3}{B}_{3}$
C. 若 ${S}_{1} + {S}_{2} = 2{S}_{3}$ ,则 ${a}_{1} + {a}_{2} = 2{a}_{3}$
D. 若 ${S}_{1}{S}_{2} = {S}_{3}^{2}$ ,则 ${a}_{1}{a}_{2} = {a}_{3}^{2}$