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题目 已知点Ｐ到两定点Ｍ(- 1 ,0 )、Ｎ(1 ,0 )的距离比为 2 ,点Ｎ到直线ＰＭ的距离为 1 ,求直线ＰＮ的方程 .解法 1 如图 1 ,作ＰＰ′⊥ｘ轴 ,ＮＮ′⊥ＭＰ,易知｜ＮＮ′｜ =1 ,｜ＭＮ｜=2 ,∠ＰＭＮ =30°.在Ｒｔ△ＰＰ′Ｎ中 ,｜ＰＰ′｜ =｜ＮＰ｜·ｓｉｎ∠ＰＮＰ′,在
The distance from the known point P to the two fixed points M(-1,0) and N(1,0) is 2, the distance from point N to the straight line PM is 1, and the equation for the straight line PN is solved. Solution 1 As shown in Fig. 1, For PP’⊥x axis, NN’⊥MP, it is easy to know |NN′| =1, |MN|=2, ∠PMN =30°. In RtΔPP′N, |PP′| =|NP|· sin∠PNP′, in