抛物线y^2=2px的焦点为F,一倾斜角为π/4直线过焦点F交抛物线于A,B两点,且|AF|>|BF|,求|AF|/|BF|的值
抛物线y^2=2px的焦点为F,一倾斜角为π/4直线过焦点F交抛物线于A,B两点,且|AF|>|BF|,求|AF|/|BF|的值
数学人气:204 ℃时间:2019-09-11 11:29:12
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过点A、B分别作直线垂直于准线,垂足分别为C、D,过点B作BH垂直AC,垂足为H.为方便起见,设AF=m,BF=n.则:DF=n,AC=m,所以AH=m-n,AB=m+n.由于三角形ABH为等腰直角三角形,所以AB²=2AH²,代入,有:m+n=√2(m-n...
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