question_answer

If \[{{A}_{1}}\] is the area of the parabola \[{{y}^{2}}=4ax\] lying between vertex and the latus rectum and \[{{A}_{2}}\]is the area between the latus rectum and the double ordinate \[x=2\]a, then \[\frac{{{A}_{1}}}{{{A}_{2}}}=\]

A)  \[2\sqrt{2-1}\]  

B)  \[\frac{1}{7}\left( 2\sqrt{2+1} \right)\]

C)  \[\frac{1}{7}\left( 2\sqrt{2-1} \right)\]     

D)  None of these