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抛物线y^2=2px(p>0)上任一点Q到顶点O的距离与到焦点F的距离之比是k,求k的取值范围.
人气:296 ℃ 时间:2019-09-29 01:15:09
解答
抛物线的参数方程是x=2pt^2 y=2pt抛物线上一点Q(2pt^2,2pt)|OQ|=2pt √(t^2+1)|QF|=2pt^2+1/2pk=(2pt √(t^2+1))/(2pt^2+1/2p)=4t√(t^2+1)/(4t^2+1)=4/√3*(√3t)√(t^2+1)/((4t^2+1))≤2/√3×(3t^2+t^2+1)/(4t^...
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