如上传的图,在平面直角坐标系x0y中,抛物线L:y=ax’-2ax-3a(a>0)与x轴交于A,B两点(点A在点B的左侧),其顶点为C,D是抛物线第四象限上一点. (1)求线段AB的长;(2)当a=1时,若△ACD的面积与ΔABD 的面积相等,求 tanㄥABD 的值:(3)延长CD交x轴于点E,当AD=DE时,将AADB沿DE方向平移得到AA'EB'.将抛物线L平移得到抛物线L',使得点A',B'都落在抛物线L'上,试判断抛物线L'与L是否交于某个定点,若是,求出该定点坐标;若不是,请说明理由.---**Image 1 Description:** * **Type:** Coordinate plane with a parabola. * **Main Elements:** * **Coordinate Axes:** x-axis and y-axis intersecting at the origin O. Arrows indicate positive directions. * **Curve:** A parabola opening upwards. * **Points:** * O: Origin (0,0). * A: Point on the negative x-axis, where the parabola intersects the x-axis. * B: Point on the positive x-axis, where the parabola intersects the x-axis. * C: The vertex of the parabola, located below the x-axis and to the right of the y-axis. * D: A point on the parabola, located in the first quadrant. * **Labels:** x, y, O, A, B, C, D. **Image 2 Description:** * **Type:** Coordinate plane with a parabola. This is labeled as a "备用图" (backup diagram). * **Main Elements:** * **Coordinate Axes:** x-axis and y-axis intersecting at the origin O. Arrows indicate positive directions. * **Curve:** A parabola opening upwards, identical in appearance to the parabola in Image 1. * **Points:** * O: Origin (0,0). * A: Point on the negative x-axis, where the parabola intersects the x-axis. * B: Point on the positive x-axis, where the parabola intersects the x-axis. * C: The vertex of the parabola, located below the x-axis and to the right of the y-axis. * D: A point on the parabola, located in the first quadrant. * **Labels:** x, y, O, A, B, C, D. * **Other Text:** 备用图 (Backup Diagram) located below the figure.