题目

（本小题满分12分）动直线y =a，与抛物线相交于A点，动 点B的坐标是。（1）求线段AB中点M的轨迹C．（2）直线l过C的焦点F,且交C于 不同的两点M、N，求线段M N的最小值。 答案：解：（1）设M的坐标为（x，y），A（，），又B得 消去，得轨迹方程为，即，M的轨迹C为顶点在原点，开口向右的抛物线。 （2）略。讨论斜率，利用弦长公式求得线段M N的最小值为4.Far, far away, there is a bad king. All his people1him. One hot day, the King goes to swim2himself in the river.Suddenly he feels very3and can’t move his hands and legs. He begins to sink. 4 , two farmers are working in the filed nearby and see everything. Of course, the farmers don’t know the man in the river is the terrible king.5the farmers jump into the river and6him.The king thanks the farmers and says, “I’m your king. Ask me for7, and I will give it to you.”“My mother and father are sick in bed,” one farmer says, “Can you give me some8to send them to a doctor?” The King agrees.Then he asks9farmer, “How about you? What do you want?” The farmer looks worried and unhappy. “10 let other people know I met you.” he says.1.A.hateB.loveC.standD.mind2.A.toB.forC.withD.by3.A.happyB.gladC.weakD.strong4.A.FriendlyB.LuckilyC.SlowlyD.Quickly5.A.ThoughB.OrC.ButD.So6.A.thankB.saveC.catchD.hug7.A.somethingB.everythingC.anythingD.nothing8.A.flowersB.timeC.moneyD.help9.A.the otherB.anotherC.otherD.others10.A.What aboutB.Why notC.PleaseD.Don’t