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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

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)

在该抛物线上,且它的横坐标为

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

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)

过点于点

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

(3)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,

的纵坐标为

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

③若,则

解得,此时是等腰直角三角形.

过点轴于点

,设

解得(舍去).

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

综上所述,存在三个满足条件的点

(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,则

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

时,四边形是平行四边形

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

时,四边形是直角梯形

(如果没求出可由)

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

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········································································· 8分

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

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

此时

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

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26.(2009年重庆市)已知:如图,在平面直角坐标系中,矩形OABC的边OAy轴的正半轴上,OCx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DDEDC,交OA于点E

(1)求过点EDC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GQAB的交点P与点CG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.

 

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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)

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53、⑴ 2000 ⑶

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52、⑴ 10 ⑵ 6V ⑶ 仍可使用,3V

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51、⑴  ⑵ 2A , ,L不正常发光

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50、⑴ A  ⑵  ⑶ W

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49、⑴ 15% ⑵ 6

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48、⑴ 指示灯应与电阻串联 ⑵  ⑶过1度

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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

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