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浙江省高中数学学业水平考试中一道解析几何题是这样的:在直角坐标系x Oy中,点A、B的坐标分别为(-1,0),(1,0),设曲线C上任一点P(x,y)满足|PA|=λ|PB|(λ>0且λ≠1)(1)求曲线C的方程,并指出曲线的形状.(2)对λ的两个不同取值λ1,λ2,记对应的曲线为C1,C2.1若曲线C1,C2关于某直线对称,求λ1,λ2的积.2若λ2>λ1>1,判断两曲线的位置关系,并说明理由.
Zhejiang Province High School mathematics academic proficiency test an analytical geometry is this: Cartesian coordinate system x Oy, the coordinates of points A, B were (-1,0), (1,0), set any point on the curve C P (x, y) satisfies | PA | = λ | PB | (λ> 0 and λ ≠ 1) (1) Find the equation for curve C and indicate the shape of the curve. (2) Two different values for λ λ1, λ2, note the corresponding curve C1, C2.1 If the curve C1, C2 about a straight line symmetry, find the product of λ1, λ2 .2 if λ2> λ1> 1, determine the relationship between the two curves and explain the reasons.