题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053105-33897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053105-31877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053105-31877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053105-68321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053105-31568.png)
(1)求b、c的值;
(2)当t为何值时,点D落在抛物线上;
(3)是否存在,使得以A、B、D为顶点的三角形与△AOP相似?若存在,求此时的值;若不存在,请说明理由;
(4)连结AC,在点P运动过程中,若以PB为直径的圆与直线AC相切,直接写出此时t的值.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-41117.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-66771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-67285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-44610.png)
解析
试题分析:(1)首先由勾股定理求得线段AC的长,然后利用△AOC∽△BOA求得线段BE、AE的长,从而求得点B的坐标;
(2)由△AOP∽△PEB根据相似三角形的性质可得PE=2,即得点D的坐标为(
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-89098.png)
(3)分0<t<8时和t>8两种情况,利用△AOC∽△BEA根据相似三角形的性质求解即可;
(4)先求得AC的解析式,设BP的中点为N,由
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-70816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-11049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-57181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-15711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-87154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-54855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-32300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-11872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-48698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-19113.png)
(1)由题意得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-93452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-66771.png)
(2)△AOP∽△PEB且相似比为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053108-14506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-89098.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053108-51284.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053108-88117.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053108-93388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053108-94926.png)
(3)①当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053109-79822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053109-99118.png)
若△POA∽△ADB
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053109-92173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053109-11213.png)
∴无解
若△POA∽△BDA,同理,解得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053110-38195.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053110-68014.png)
若△POA∽△ADB
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053109-92173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053110-35110.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053110-60073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053111-36336.png)
若△POA∽△BDA,同理,解得无解
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053111-56679.png)
(4)∵A(0,4),C(8,0)
∴AC的解析式为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053111-91191.png)
设BP的中点为N,由
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-70816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-11049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-57181.png)
过点N作FN//AC交y轴于点F,过点F作FH⊥AC于点H
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053111-93108.jpg)
可设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-15711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053106-87154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-54855.png)
由△AFH∽△ACO可得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-32300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-11872.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-48698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053107-19113.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053111-23964.png)
整理得31t2-336t+704=0,解得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053112-35801.png)
点评:本题知识点多,综合性强,难度较大,一般是中考压轴题,主要考查学生对二次函数的性质的熟练掌握情况.
核心考点
试题【如图,在平面直角坐标系xOy中,抛物线过点A(0,4)和C(8,0),P(t,0)是轴正半轴上的一个动点,M是线段AP的中点,将线段MP绕点P顺时针旋转90°得】;主要考察你对二次函数定义等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053100-62184.png)
A.x<1 | B.x>1 | C.x>-2 | D.-2<x<4 |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053057-40220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053057-30499.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053057-36816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053053-57067.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053049-14924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053049-35795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053044-75558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053044-69778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053044-75558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053045-72941.png)
最新试题
- 1Michel is a young girl who works for the police ____ a handw
- 2梅兰竹菊四君子,千百年来以其清雅淡泊的品质,一直为世人所钟爱,成为美好人格品性的象征。请模仿下面例句,从梅、竹、菊中任选
- 32014年5月19日是我国第二十四个“全国助残日”。随着经济发展和社会进步,我国的残疾人保障事业也取得了显著的成绩。这体
- 4下列有关种群增长的“S”型曲线的叙述中,错误的是[ ]A.通常自然界中的种群增长曲线最终呈“S”型B.达到K值时
- 5用滑轮组将陷在泥中汽车拉出来,试在下图中画出最省力的绕绳方法。
- 6不同的材料具有不同的性能,将下列材料具有的性能用短线连起来: 材料种类
- 7马六甲海峡是连接太平洋和印度洋的重要海上通道.______.
- 8 绘画艺术是人类经济、社会发展和信息传播的载体,借此我们可以了解历史发展各阶段的文化、社会状况。图一《女史箴
- 9我们吃的水果中,杏、桃属于果实。果实的组成是A.果皮与种皮B.种子与种皮C.果皮与种子D.子房与胚珠
- 10细胞分裂的过程中染色体变化的顺序是( )(1)染色体平均分成两等份,向细胞两极移动 (2)染色体分别进入两个细胞核
热门考点
- 1I can’t play _____basketball but I can play ___ piano. A.
- 2bg某金属与足量的稀硫酸反应,生成该金属的三价正盐和ag氢气。则该金属的相对原子质量为[ ]A.2b/a B.3
- 3牛顿出生于公元1643年,我们记作+1643,那么阿基米德出生于公元前287年,可记作______.
- 4已知:如图,在正方形ABCD外取一点E,连接AE、BE、DE.过点A作AE的垂线交DE于点P.若AE=AP=1,PB=.
- 5A、B、C、D四种元素均为短周期元素,其原子半径依次减小,它们的气态氢化物分子所含的电子数相同,C元素原子的K层电子数与
- 6糖原、核酸和淀粉酶的基本单位分别是[ ]A.碱基、单糖、氨基酸B.葡萄糖、碱基、氨基酸C.葡萄糖、核苷酸、氨基酸
- 7盐酸、硫酸和硝酸是中学阶段常见的三种强酸。请就三者与金属铜的反应情况,回答下列问题:(1)①在100 mL 18 mol
- 8—Why is ______ easy for such a young girl to learn three for
- 9下列方程组中,二元一次方程组一共有几个(1)(2)(3)(4)
- 10有人提出,如果把冷战时期重新定义为“长时期的和平”倒是颇为耳目一新的。上述对冷战重新定义的主要出发点是A.美国马歇尔计划