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[几何] 一个椭圆斜率恒定问题

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snowblink posted 2022-12-11 23:03 |Read mode
Last edited by snowblink 2022-12-12 10:16已知椭圆$\frac{{x}^{2}}{4}\mathrm{{+}}{y}^{2}\mathrm{{=}}{1}$,点${P}\left({2\mathrm{,}1}\right){\mathrm{,}}{Q}\left({1\mathrm{,}1}\right)$,过$Q$作直线$l$交椭圆于$A\mathrm{,}B$两点,直线$PA\mathrm{,}PB$交椭圆于$
M\mathrm{,}N
$两点,求证:直线$
MN\mathrm{//}x
$轴.

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