过抛物线y=-1/4x²的焦点作倾斜角为a的直线l与抛物线交于A,B两点,且|AB|=8,求倾斜角a!
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![过抛物线y=-1/4x²的焦点作倾斜角为a的直线l与抛物线交于A,B两点,且|AB|=8,求倾斜角a!](/uploads/image/z/9304202-2-2.jpg?t=%E8%BF%87%E6%8A%9B%E7%89%A9%E7%BA%BFy%3D-1%2F4x%26%23178%3B%E7%9A%84%E7%84%A6%E7%82%B9%E4%BD%9C%E5%80%BE%E6%96%9C%E8%A7%92%E4%B8%BAa%E7%9A%84%E7%9B%B4%E7%BA%BFl%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%BA%A4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E4%B8%94%7CAB%7C%3D8%2C%E6%B1%82%E5%80%BE%E6%96%9C%E8%A7%92a%21)
过抛物线y=-1/4x²的焦点作倾斜角为a的直线l与抛物线交于A,B两点,且|AB|=8,求倾斜角a!
过抛物线y=-1/4x²的焦点作倾斜角为a的直线l与抛物线交于A,B两点,且|AB|=8,求倾斜角a!
过抛物线y=-1/4x²的焦点作倾斜角为a的直线l与抛物线交于A,B两点,且|AB|=8,求倾斜角a!
过抛物线y=-1/4x²的焦点作倾斜角为a的直线l与抛物线交于A,B两点,且|AB|=8,求倾斜角a!
解析:∵抛物线y=-1/4x^2,其焦点为F(-1/16,0), p=1/8
设直线l的倾角为a
由抛物线极坐标方程ρ=ep/(1-ecosa)
∴|FA|=p/(1-cosa), |FB|=p/(1-cos(π+a))
|AB|= p/(1-cosa)+p/(1+cosa)=2p/(sina)^2=8
∴(sina)^2=p/4=1/32==>sina=±√2/8
∴倾斜角a=arcsin√2/8或π- arcsin√2/8
tana=3/2