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1原题的分析及解答10年广东文科卷第21题原题如下:已知曲线C_n:y=nx~2,点P_n(x_n,y_n)(x_n>0,y_n>0)是曲线C_n上的点(n=1,2,…).(1)试写出曲线C_n在点P_n处的切线l_n的方程,并求出l_n与y轴的交点Q_n的坐标;(2)若原点O(0,0)到l_n的距离与线段P_nQ_n的长度之比取得最大值,试求点P_n的坐标(x_n,y_n);(3)设m与k为两个给定的不同的正整数,
The original title is as follows: Known curve C_n: y = nx ~ 2, the point P_n (x_n, y_n) (x_n> 0, y_n> 0) is the curve C_n (N = 1, 2, ...). (1) Write out the equation of the tangent line l_n of the curve C_n at the point P_n and find the coordinate of the intersection point Q_n between the axis l_n and the y axis. (2) If the origin O (X_n, y_n); (3) Let m and k be two given different positive integers, and then find the coordinate of the point P_n