...已知抛物线y2=4x的焦点为F,过F的直线交抛物线于M、N两点,其准线l...
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发布时间：2024-10-06 01:39
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时间：2024-11-20 14:08
（1）证明：抛物线焦点坐标为F（1，0），准线方程为x=-1…．（2分）
设直线MN的方程为x=my+1，M、N的坐标分别为(y124，y1)，(y224，y2)
由x＝my+1y2＝4x?y2?4my?4＝0，∴y1+y2=4m，y1y2=-4…..（4分）
设KM和KN的斜率分别为k1，k2，显然只需证k1+k2=0即可．
∵K（-1，0）
∴k1+k2＝y1y214+1+y2y224+1＝4(y1+y2)(y1y2+4)(y21+4)(y21+4)＝0…（6分）
（2）解：设M、N的坐标分别为(y124，y1)，(y224，y2)，
由M，O，P三点共线可得P点的坐标为(?1，?4y1)，
同理可由N，O，Q三点共线可求出Q点坐标为(?1，?4y本回答由提问者推荐已赞过已踩过你对这个回答的评价是？评论收起 ._1uevpeq{zoom:1;background-color:#fff;border:0;margin-bottom:10px;padding:30px 0 20px 42px;position:relative}._1uevpeq.ec-1841{padding:20px 0}._1uevpeq.ec-2246{padding:20px 0 10px}.ec-1841 .y7we4hu{font-size:16px;margin-bottom:-5px}.y7we4hu{color:#7a8f9a;height:25px;line-height:25px;overflow:hidden;position:relative}.y7we4hu h2{margin:0;padding:0}.y7we4hu:after{clear:both;content:" ";display:block;height:0;visibility:hidden}a.tycfu7u{color:#666;float:right;font-size:12px;margin-left:8px;text-decoration:none}.hhhv6ex{color:#666;font-size:13px;line-height:normal;line-height:20px;margin-top:10px}.vnsdjzp{margin-top:15px;position:relative}.vnsdjzp h3{font-weight:400;padding:0}.vnsdjzp a{text-decoration:none}.vnsdjzp em{color:#d81419;font-style:normal}.ec-2246 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