26.如图16.在平面直角坐标系中.直线与轴交于点.与轴交于点.抛物线经过三点. (1)求过三点抛物线的解析式并求出顶点的坐标, (2)在抛物线上是否存在点.使为直角三角形.若存在.直接写出点坐标,若不存在.请说明理由, (3)试探究在直线上是否存在一点.使得的周长最小.若存在.求出点的坐标,若不存在.请说明理由. 解:(1)直线与轴交于点.与轴交于点. .························································································· 1分 点都在抛物线上. 抛物线的解析式为························································ 3分 顶点······························································································· 4分 (2)存在··············································································································· 5分 ············································································································· 7分 ············································································································ 9分 (3)存在·············································································································· 10分 理由: 解法一: 延长到点.使.连接交直线于点.则点就是所求的点. ····················································································· 11分 过点作于点. 点在抛物线上. 在中.. .. 在中.. ..··············································· 12分 设直线的解析式为 解得 ································································································ 13分 解得 在直线上存在点.使得的周长最小.此时.··· 14分 解法二: 过点作的垂线交轴于点.则点为点关于直线的对称点.连接交于点.则点即为所求.················································································ 11分 过点作轴于点.则.. . 同方法一可求得. 在中...可求得. 为线段的垂直平分线.可证得为等边三角形. 垂直平分. 即点为点关于的对称点.············································· 12分 设直线的解析式为.由题意得 解得 ································································································ 13分 解得 在直线上存在点.使得的周长最小.此时.··· 14分 查看更多

 

题目列表(包括答案和解析)

计算:
(1)(
12
+
18
)×2
6

(2)(4
15
-3
5
)÷2
5

(3)(2
5
+3)(2
5
-2)

(4)(
6
+
3
)2

(5)(2
6
-3
2
)2

(6)(3
3
+2
2
)(3
3
-2
2
)

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列方程或方程组解应用题:
世界上最长最快的高速铁路武广高速于2009年12月26日开通运营,预计高速列车在武汉、广州间单程直达运行时间为3小时.某次试车时,试验列车由武汉到广州的行驶时间比预计时间多用了36分钟,由广州返回武汉的行驶时间与预计时间相同.如果这次试车时,由广州返回武汉比去广州时平均每分钟多行驶1千米,那么这次试车时由武汉到广州的平均速度是每小时多少千米?

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2008年12月26日,中国海军舰艇编队起航赴索马里海域执行护航任务,这次执行任务的舰艇是从南海舰队中选择的:从A“太仓”号、B“徽山湖”号、C“抚仙湖”号中随机选择一艘补给舰;再从D“武汉”号、E”兰州“号、F”海口“号中随机选择两艘导弹驱逐舰.
(1)请用树状图或列举法说明中国海军舰艇编队符合上述条件的所有可能的选择方式(用字母表示);
(2)在(1)的选择方式中,求中国海军舰艇编队恰好选中B“徽山湖”号,同时选中D“武汉”号和 F“海口”号两艘导弹驱逐舰的概率.

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精英家教网2009年12月26日开通的“武广高铁”客运专线,使武汉到广州的时间比原先快速列车缩短了8小时,武汉到广州的距离为1068.6千米,若客运专线列车的速度是特快列车速度的3倍,那么客运专线列车的速度是多少?

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(2013•沈阳一模)2012年12月26日京广高铁全线通车.一列往返于北京和广州的火车,沿途要经过石家庄、郑州、武汉、长沙四站,铁路部门要为这趟列车准备印制(  )种车票.

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