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本文拟对2013年全国高中数学联赛湖北省预赛高二年级第6题进行探究.试题如图1,设F为椭圆C:x2/4+y2/3=1的右焦点,过椭圆C外一点P作椭圆C的切线,切点为M,若∠PFM=90°,求点P的轨迹方程.1.探究试题本身的解法解法1由于点P由点M的运动引起,因此若设点M的坐标为M(2cosθ,1/23sinθ),则点P可以用θ表示,从而可求得点P的轨迹方程.事实上,直
This article intends to explore the sixth national high school mathematics league in Hubei Province in the sixth grade of senior high school in 2013. As shown in Figure 1, let F be the right focal point of elliptic C: x2 / 4 + y2 / 3 = 1, For the tangent of ellipse C, the tangent point is M, if ∠PFM = 90 °, find the path equation of point P. 1.Examine the solution of the test item itself Solution 1 Since the point P is caused by the movement of the point M, if the point M The coordinates of M (2cosθ, 1 / 23sinθ), then the point P can be expressed as θ, which can be obtained point P trajectory equation.In fact, the straight