26．解：(1)由已知，得，，

，

．

．············································································································ (1分)

设过点的抛物线的解析式为．

将点的坐标代入，得．

将和点的坐标分别代入，得

··································································································· (2分)

解这个方程组，得

故抛物线的解析式为．··························································· (3分)

(2)成立．························································································· (4分)

点在该抛物线上，且它的横坐标为，

点的纵坐标为．······················································································· (5分)

设的解析式为，

将点的坐标分别代入，得

　 解得

的解析式为．········································································ (6分)

，．··························································································· (7分)

过点作于点，

则．

，

．

又，

．

．

．··········································································································· (8分)

．

(3)点在上，，，则设．

，，．

①若，则，

解得．，此时点与点重合．

．··········································································································· (9分)

②若，则，

解得 ，，此时轴．

与该抛物线在第一象限内的交点的横坐标为1，

点的纵坐标为．

．······································································································· (10分)

③若，则，

解得，，此时，是等腰直角三角形．

过点作轴于点，

则，设，

．

．

解得(舍去)．

．··········································· (12分)

综上所述，存在三个满足条件的点，

即或或．

(2009年重庆綦江县)26．(11分)如图，已知抛物线经过点，抛物线的顶点为，过作射线．过顶点平行于轴的直线交射线于点，在轴正半轴上，连结．

(1)求该抛物线的解析式；

(2)若动点从点出发，以每秒1个长度单位的速度沿射线运动，设点运动的时间为．问当为何值时，四边形分别为平行四边形？直角梯形？等腰梯形？

(3)若，动点和动点分别从点和点同时出发，分别以每秒1个长度单位和2个长度单位的速度沿和运动，当其中一个点停止运动时另一个点也随之停止运动．设它们的运动的时间为，连接，当为何值时，四边形的面积最小？并求出最小值及此时的长．

*26．解：(1)抛物线经过点，

·························································································· 1分

二次函数的解析式为：·················································· 3分

(2)为抛物线的顶点过作于，则，

··················································· 4分

当时，四边形是平行四边形

················································ 5分

当时，四边形是直角梯形

过作于，则

(如果没求出可由求)

····························································································· 6分

当时，四边形是等腰梯形

综上所述：当、5、4时，对应四边形分别是平行四边形、直角梯形、等腰梯形．·· 7分

(3)由(2)及已知，是等边三角形

则

过作于，则········································································· 8分

=·································································································· 9分

当时，的面积最小值为··································································· 10分

此时

······················································ 11分

26．(2009年重庆市)已知：如图，在平面直角坐标系中，矩形OABC的边OA在y轴的正半轴上，OC在x轴的正半轴上，OA=2，OC=3．过原点O作∠AOC的平分线交AB于点D，连接DC，过点D作DE⊥DC，交OA于点E．

(1)求过点E、D、C的抛物线的解析式；

(2)将∠EDC绕点D按顺时针方向旋转后，角的一边与y轴的正半轴交于点F，另一边与线段OC交于点G．如果DF与(1)中的抛物线交于另一点M，点M的横坐标为，那么EF=2GO是否成立？若成立，请给予证明；若不成立，请说明理由；

(3)对于(2)中的点G，在位于第一象限内的该抛物线上是否存在点Q，使得直线GQ与AB的交点P与点C、G构成的△PCG是等腰三角形？若存在，请求出点Q的坐标；若不存在，请说明理由．

25.(2009年北京)如图，在平面直角坐标系中，三个机战的坐标分别为

，，，延长AC到点D,使CD=,过点D作DE∥AB交BC的延长线于点E.

(1)求D点的坐标；

(2)作C点关于直线DE的对称点F,分别连结DF、EF，若过B点的直线将四边形CDFE分成周长相等的两个四边形，确定此直线的解析式；

(3)设G为y轴上一点，点P从直线与y轴的交点出发，先沿y轴到达G点，再沿GA到达A点，若P点在y轴上运动的速度是它在直线GA上运动速度的2倍，试确定G点的位置，使P点按照上述要求到达A点所用的时间最短。(要求：简述确定G点位置的方法，但不要求证明)

53、⑴ 2000 ⑵ 　⑶

52、⑴ 10， ⑵ 6V ⑶ 仍可使用，3V

51、⑴ 　⑵ 2A ， ，L不正常发光

50、⑴ A　 ⑵ 　⑶ W

49、⑴ 15% ⑵ 6

48、⑴ 指示灯应与电阻串联 ⑵ 　⑶过1度

47、⑴ 　⑵ 　⑶ 9W　 ⑷当电动机被卡住其发热功率将大大提高，若及时切断电源，会使电动机温度很快升高，极易烧坏电动机