1 常量与变量,相互可转换 常量与变量是相对的,在一定条件下,两者可互相转换。 例1.解方程(x~2+6x+10)~(1/2)+(x~2-6x+10)~(1/2)=6 3~(1/2)。 解:变换原方程的结构,有 ((x+3)~2+y~2)~(1/2)+((x-3)~2+y~2)~(1/2)=2 3~(1/2)(其中y~2=1)它表明:动点P(x,y)到两定点F_1(-3,0)和F_2(3,0)的距离之和为2(3 3~(1/2))。这就是椭圆。其标准方程为 1 constants and variables, mutual convertible constants and variables are relative, under certain conditions, the two can be converted to each other. Example 1. Solution equation (x~2+6x+10)~(1/2)+(x~2-6x+10)~(1/2)=6 3~(1/2). Solution: Transform the structure of the original equation, ((x+3)~2+y~2)~(1/2)+((x-3)~2+y~2)~(1/2)=2 3~(1/2) (where y~2=1) It indicates that the sum of the distance from the moving point P(x,y) to the two fixed points F_1(-3,0) and F_2(3,0) is 2 ( 3 3~(1/2)). This is the ellipse. The standard equation is