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
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