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八五年高考文科数学试题中有一道解析几何题:“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l对称的圆的方程”,此题满分15分,标准答案如下: 解法一已知圆c的方程是x~2+y~2+4x-12y+39=0它可写成(x+2)~2+(y-6)~2=1,因此它的圆心为p(-2,6),半径为1,设所求圆的圆心为p′(a,b),则pp′的中点((a-2)/2,(b+6)~2)应在直线l上,故有:3((a-2)/2))-4((b+6)/2))+5=0即 3a-4b-20=0(1)
In the mathematics test of the eight-year college entrance examination in the liberal arts, there is an analytic geometry problem: “A circle is known as 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 symmetry of the circle ", this question is out of 15 points, the standard answer is as follows: The solution of a known circle c is x~2+y~2+4x-12y+39=0 which can be written as (x +2)~2+(y-6)~2=1, so its center is p(-2,6) and its radius is 1. If the center of the circle is p’(a,b), then pp The middle point of (’(a-2)/2, (b+6)~2) should be on the straight line l, so it is: 3((a-2)/2))-4((b+6)/ 2)) +5=0 ie 3a-4b-20=0(1)