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如果曲线中某些量不依赖于变化元素而存在,则称为定值.求定值是解析几何中颇有难度的一类问题,蕴含了动静相依的辩证关系,解决这类问题时,要善于动中求静、变中求定.本文探讨一个定值问题的求解方法,并进行拓展探究.一、题目及解法已知圆C过点P(1,1),且与圆M:(x+2)2+(y+2)2=r2(r>0)关于直线x+y+2=0对称.(1)求圆C的方程;(2)过点P作两条相异的直线与圆C相交于A,B两点,且直线PA和PB的倾斜角互补,O为坐标原点,试判断直线OP和AB是否平行?请说明
If some of the curve does not depend on the changing elements exist, then called the fixed value. Evaluation is analytic geometry quite difficult a class of problems, contains the dialectical relationship between the static and dynamic dependencies, to solve such problems, we must Good at moving in seeking static, variable in. This paper discusses a solution to the problem of fixed value, and to explore. First, the problem and solution known C over the point P (1,1), and the circle M :( x + 2) 2+ (y + 2) 2 = r2 (r> 0) Symmetry with respect to the line x + y + 2 = 0. (1) Find the equation of the circle C; Intersects the circle C at A and B points, and the inclination angles of the lines PA and PB are complementary, and O is the origin of coordinates. Try to judge whether the lines OP and AB are parallel or not.