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纵观近几年高考数学理科试题,其中对解析几何中椭圆的切线相关问题的考查比较典型,本文从椭圆的切线方程开始,研究与椭圆切线相关的定值、定点、定轨迹问题。问题:已知椭圆C:x~2/a~2+y~2/b~2=1(a>b>0),若动点P(x_0,y_0)为椭圆外一点,且点P到椭圆C的两条切线相互垂直,求点P的轨迹方程。
Throughout the mathematics science subjects in recent years college entrance examination examinations, which parse the geometry of the oval tangent related problems more typical test, starting from the tangent elliptic equation, the ellipse tangent related to the valuation, fixed point, trajectory problems. Problem: Known oval C: x ~ 2 / a ~ 2 + y ~ 2 / b ~ 2 = 1 (a> b> 0). If the moving point P (x_0, y_0) is a point outside the ellipse, The two tangent lines of ellipse C are perpendicular to each other and find the path equation of point P.