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一、定义法求曲线轨迹方程是解析几何的两个基本问题之一,求符合某种条件的动点轨迹方程,其实质就是利用题设中的几何条件,通过坐标互化将其转化为寻求变量之间的关系.在求与圆锥曲线有关的轨迹问题时,要特别注意圆锥曲线的定义在求轨迹中的作用,只要动点满足已知曲线定义时,通过待定系数法就可以直接得出方程.例1已知△ABC中,∠A,∠B,∠C所对应的边为a,b,c且a>b,a,c,b成等差数列,|AB|=2,求顶点C的轨迹方程解:|BC|+|CA|=2|AB|=4>2,由椭圆的定义可知,点C的轨迹是以A、B为焦点的椭圆,其长轴为4,焦距为2,短轴
First, the definition of law to find the curve Trajectory equation analytic geometry is one of the two basic problems, to meet certain conditions of the dynamic point trajectory equation, the essence is to use the geometry of the problem set by the coordinate each other to turn it into seeking When discussing the trajectory problem related to the conic curve, pay special attention to the conic curve’s definition in finding the trajectory. As long as the moving point satisfies the known curve definition, it can be directly obtained by the undetermined coefficient method Equation 1 In ABC, the edges corresponding to ∠A, ∠B, ∠C are a, b, c and a> b, a, c, b are equal difference sequences, | AB | = 2, The trajectory equation of vertex C is: | BC | + | CA | = 2 | AB | = 4> 2. From the definition of ellipse, the locus of point C is an ellipse focusing on A and B, Focal length is 2, short axis