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中心对称是对称问题中的常见形式.若求某曲线关于一点对称的曲线所对应的方程,可由相关点法直接求出.那么,如果两曲线的对称中心未给出,要求我们证明或求解,如何应对? 1.互为对称式例1 已知曲线C的方程是y=x~3-x,将C沿x轴、y轴的正向分别平行移动t,s单位个长度后,得到曲线C1,若曲线C与C1的关于点A成中心对称,猜想点A的坐标,并证明你的结论.
Center symmetry is a common form of symmetry problem. If the equation corresponding to a point-symmetrical curve is obtained, it can be directly determined by the correlation point method. Then, if the symmetry center of the two curves is not given, we need to prove or solve it. How to deal with it? 1. Symmetrical each other Example 1 The equation of the known curve C is y=x~3-x. Move the C along the positive direction of the x-axis and y-axis in parallel and move t. After s is a unit of length, obtain the curve. C1, if curve C and C1 are center symmetrical about point A, guess the coordinates of point A and prove your conclusion.