8．一个函数的图象关于轴成轴对称图形时，称该函数为偶函数． 那么在下列四个函数①；②；③；④中，偶函数是 　　　　 (填出所有偶函数的序号)．

7．如图3，已知，∠1=130^o，∠2=30^o，则∠C=　　 　　　　　．

6．如图2，△ABC向右平移4个单位后得到△A′B′C′，则A′点的坐标是　　 　　　 ．

5．如图1，已知点C为反比例函数上的一点，过点C向坐标轴引垂线，垂足分别为A、B，那么四边形AOBC的面积为 　　　　　　．

4．一个圆锥的母线长为5cm，底面圆半径为3 cm，则这个圆锥的侧面积是　　 　　cm²(结果保留)．

3．已知△ABC中，BC=6cm，E、F分别是AB、AC的中点，那么EF长是　 　　 cm．

2．因式分解：　　　　　 ．

1．3的倒数等于　 　　　　．

25．解：(1)依条件有，．

由知．

∴由得．

∴．

将的坐标代入抛物线方程，

得．

∴抛物线的解析式为．····································································· 3分

(2)设，，．

∴

设，则

∴，(舍去)

此时点与点重合，，，，

则为等腰梯形．······························································································· 3分

(3)在射线上存在一点，在射线上存在一点．

使得，且成立，证明如下：

当点如图①所示位置时，不妨设，过点作，，，垂足分别为．

若．由得：

，

．

又

．············································································································· 2分

当点在如图②所示位置时，

过点作，，

垂足分别为．

同理可证．

．

又，

，

．············································································································· 1分

当在如图③所示位置时，过点作，垂足为，延长线，垂足为．

同理可证．

．············································································································· 1分

注意：分三种情况讨论，作图正确并给出一种情况证明正确的，同理可证出其他两种情况的给予4分；若只给出一种正确证明，其他两种情况未作出说明，可给2分，若用四点共圆知识证明且证明过程正确的也没有讨论三种情况的．只给2分．

24．解：(1)．

其证明如下：

∵是的平分线，．

∵，∴．

∴．

∴．

同理可证．

∴．······················································· 3分

(2)四边形不可能是菱形，若为菱形，则，而由(1)可知，在平面内过同一点不可能有两条直线同垂直于一条直线．············································································· 3分

(3)当点运动到中点时，，，则四边形为，要使为正方形，必须使．

∵，∴，∴是以为直角的直角三角形，

∴当点为中点且是以为直角的直角三角形时，

四边形是正方形．····························································································· 3分