已知抛物线方程 y²=4x ,若过焦点F且倾斜角为60°的直线m交抛物线与A,B两点,点M在抛物线的准线上,此时MF,MA,MB的斜率为kMA.KMF,KMB,求证; 2KMF=KMA+KMB
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![已知抛物线方程 y²=4x ,若过焦点F且倾斜角为60°的直线m交抛物线与A,B两点,点M在抛物线的准线上,此时MF,MA,MB的斜率为kMA.KMF,KMB,求证; 2KMF=KMA+KMB](/uploads/image/z/5059301-5-1.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BF%E6%96%B9%E7%A8%8B+y%26%23178%3B%3D4x+%2C%E8%8B%A5%E8%BF%87%E7%84%A6%E7%82%B9F%E4%B8%94%E5%80%BE%E6%96%9C%E8%A7%92%E4%B8%BA60%C2%B0%E7%9A%84%E7%9B%B4%E7%BA%BFm%E4%BA%A4%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E7%82%B9M%E5%9C%A8%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E5%87%86%E7%BA%BF%E4%B8%8A%2C%E6%AD%A4%E6%97%B6MF%2CMA%2CMB%E7%9A%84%E6%96%9C%E7%8E%87%E4%B8%BAkMA.KMF%2CKMB%2C%E6%B1%82%E8%AF%81%EF%BC%9B+2KMF%3DKMA%2BKMB)
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已知抛物线方程 y²=4x ,若过焦点F且倾斜角为60°的直线m交抛物线与A,B两点,点M在抛物线的准线上,此时MF,MA,MB的斜率为kMA.KMF,KMB,求证; 2KMF=KMA+KMB
已知抛物线方程 y²=4x ,若过焦点F且倾斜角为60°的直线m交抛物线与A,B两点,
点M在抛物线的准线上,此时MF,MA,MB的斜率为kMA.KMF,KMB,求证; 2KMF=KMA+KMB
已知抛物线方程 y²=4x ,若过焦点F且倾斜角为60°的直线m交抛物线与A,B两点,点M在抛物线的准线上,此时MF,MA,MB的斜率为kMA.KMF,KMB,求证; 2KMF=KMA+KMB
设x=y√3/3+1
x=y√3/3+1
y²=4x
y²-4√3y/3-4=0
设A(x1,y1)B(x2,y2)
y1+y2=4√3/3
y1y2=-4
设M(-1,m)
kMF=m/-2
kMA=(y1-m)/(x1+1)
kMB=(y2-m)/(x2+1)
kMA+kMB=(y1-m)/(x1+1)+(y2-m)/(x2+1)
=[y1+y2-2m+y2x1+y1x2-m(x1+x2)]/(x1x2+x1+x2+1)
={y1+y2-2m+y1y2(y1+y2)/4-m[(y1+y2)²-2y1y2]/4}/{y1²y2²+[(y1+y2)²-2y1y2]/4+1}
={4√3/3-4√3/3-[(4√3/3)²+8]m/4-2m}/{1+[(4√3/3)²+8]m/4+1}
=-m=2kMF