12.
如图,将矩形OABC置于平面直角坐标系中,点A的坐标为(0,4),点C在x轴上,点D(3$\sqrt{5}$,1)在BC上,将矩形OABC沿AD折叠压平,使点B落在坐标平面内,设点B的对应点为点E.若抛物线y=ax2-4$\sqrt{5}$ax+10(a≠0且a为常数)的顶点落在△ADE的内部,则a的取值范围是( )
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| A. | $\frac{2}{5}<a<\frac{13}{20}$ | B. | $\frac{2}{5}<a<\frac{11}{20}$ | C. | $\frac{11}{20}<a<\frac{3}{5}$ | D. | $\frac{3}{5}<a<\frac{13}{20}$ |