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2017年全国高中数学联赛浙江省预赛第12题为:已知椭圆x~2/6+y~2/2=1的右焦点为F,过F的直线y=k(x-2)交椭圆于P、Q两点(k≠0).若PQ的中点为N,O为原点,直线ON交直线x=3于M.(1)求∠MFQ的大小;(2)求PQ/MF的最大值.此题第一问的答案为∠MFQ=90°.经过深入研究,笔者发现:将原题中的椭圆一般化,其余条件不变,该结论仍然成立,进一步研究发现,在双曲线、
The twelfth national title of Zhejiang Province Preliminary Contest in 2017 National High School Math League is: It is known that the right focus of the ellipse x ~ 2/6 + y ~ 2/2 = 1 is F, the straight line of F is y = k If the midpoint of PQ is N, O is the origin, the line ON intersects the straight line x = 3 in M. (1) Find the size of ∠MFQ; (2) Find PQ / MF The first answer to this question is ∠MFQ = 90 ° .After in-depth study, I found that: the oval in the original title generalization, the remaining conditions remain unchanged, the conclusion is still established, further research found that in the double curve,