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关于点或直线对称问题是高考热点内容之一。这类问题解法具有一般的变换式。下面以高考题为例说明之。 1.求关于点对称的曲线方程问题 易知任意点(x,y)关于定点(x_0,y_0)对称的点的坐标为(2x_0-x,2y_0-y)。因此, 和曲线F(x,y)=0关于点(x_0,y_0)对称的曲线方程是F(2x_0-x,2y_0-y)=0。我们用此变换式,可解这类题。
Symptoms about point or line symmetry are one of the hot topics of college entrance examination. The solution to this type of problem has a general transformation. The following is an example of a college entrance exam question. 1. Find the problem about the point symmetry curve equation It is easy to know the coordinates of any point (x, y) symmetric about the fixed point (x_0, y_0) is (2x_0-x, 2y_0-y). Therefore, the equation of the curve symmetric with the curve F(x,y)=0 with respect to the point (x_0,y_0) is F(2x_0-x, 2y_0-y)=0. We use this transformation to solve such questions.