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本刊85年第4期《从一九八五年一道高考数学试题谈起》一文中,对85年高考文科数学第7题提供了8种解法,并一一作了评述。本人参加了江苏省高考文科数学试卷的评阅工作,在考生给出的该题解法中,发现了两种很“怪”的解法,现在写出来作为该文的补充。原题已知一个圆C:x~2+y~2+4x-12y+39=0和一条直线l:3x-4y+5==0,求圆C关于直线f对称的圆的方程。解法一从l的方程得y=1/4(3x+5),代入C的方程得 25x~2-50x+409=0。 (1) 设方程(1)的两根为x_1、x_2,用韦达
In the 4th issue of “A Mathematics Exam Question in a College Entrance Examination in 1985” published in the 85th issue of this journal, eight solutions to the seventh problem of the liberal arts mathematics in the 85-year college entrance examination were provided and reviewed one by one. I participated in the review of the mathematics test of the Jiangsu Provincial College Entrance Examination. In the solution given by the candidate, I found two very strange solutions. Now I write it as a supplement to this article. The original title is known as a circle C:x~2+y~2+4x-12y+39=0 and a line l:3x-4y+5==0. The equation for the circle C with respect to the line f is symmetric. The solution from the equation of l is y=1/4(3x+5), and the equation substituted into C is 25x~2-50x+409=0. (1) Let the two roots of equation (1) be x_1, x_2, with Vedic