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数学中的探究性问题一般是条件开放或结论开放,高考中的探究性问题主要考查学生是否具备解决开放度较小的数学问题的能力,即要求考生综合运用学到的基本知识、基本技能和基本方法创造性地解决问题。本文仅对解析几何探究性问题进行讨论。一、以逆向思考的方法探究结论成立的条件例1在平面直角坐标系xOy中,点A(0,3),圆C的方程是(x-a)~2+(y-2a+4)~2=1,试求参数a的取值范围,使圆C上存在点M,使MA=2MO成立。解析设M为(x,y),因为MA=2MO,所以(?)=2(?)。整理,得一个圆的方程x~2+(y+1)~1=4,设为圆D。
Inquiry problems in mathematics are generally open-minded or open-ended. Inquiring questions in the college entrance examination mainly examine whether students have the ability to solve mathematical problems with less openness, that is, they require students to comprehensively apply the basic knowledge learned, basic skills and The basic method to solve the problem creatively. This article discusses only analytic geometry inquiries. First, the method of reverse thinking to explore the conditions for the establishment of cases Example 1 rectangular Cartesian coordinate system xOy point A (0,3), the circle C equation is (xa) ~ 2 + (y-2a +4) ~ 2 = 1, try to find the value of parameter a, so that there is a point M on the circle C, MA = 2MO holds. Let M be (x, y), because (MA) = 2MO, so (?) = 2 (?). Finishing, get a circle equation x ~ 2 + (y +1) ~ 1 = 4, set to circle D.