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真题再现如图1,在平面直角坐标系xOy中,M、N分别是椭圆(x~2)/4+(y~2)/2=1的顶点,过坐标原点的直线交椭圆于P、A两点,其中点P在第一象限.过P作x轴的垂线,垂足为C,连接AC,并延长交椭圆于点B.设直线PA的斜率为k.图1(1)(2)略(3)对任意的k>0,求证:PA⊥PB.我们知道,对于问题(3)PA⊥PB的等价条件
Reproduce the Zhenti in Figure 1, Cartesian coordinates in the plane xOy, M, N are elliptic (x ~ 2) / 4 + (y ~ 2) / 2 = 1 vertices, A two, where the point P in the first quadrant. P for the x-axis perpendicular to the line, the foot is C, connected to AC, and extend the intersection ellipse at point B. Set the slope of the straight line PA k. (2) Slightly (3) For any k> 0, verify: PA ⊥ PB. We know that for the problem (3) the equivalent condition of PA ⊥ PB