题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025843-32090.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025843-76041.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025844-80610.gif)
(1)求实数a,b,k的值;
(2)过抛物线上点A作直线AC∥x轴,交抛物线于另一点C,求所有满足△EOC∽△AOB的点E的坐标.
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025844-11077.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025844-80610.gif)
所以k="4." 故双曲线的函数表达式为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025844-85955.gif)
设点B(t,
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025844-42192.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025844-20968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025844-40614.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025844-69116.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-21197.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-29929.gif)
于是,直线AB与y轴的交点坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-27358.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-48070.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-55651.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-54530.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-22291.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-64571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-64571.gif)
因为点A,B都在抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025843-32090.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025843-76041.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-45371.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-91479.gif)
(2)如图,因为AC∥x轴,所以C(
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-92291.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-62613.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-62613.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-69258.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-75385.jpg)
设抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025843-32090.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025843-76041.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-17674.gif)
因为∠COD=∠BOD=
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-93993.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-60962.gif)
(i)将△
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025847-80925.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-60962.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025847-67849.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025847-13642.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-64571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025847-59990.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025847-97589.gif)
延长
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025848-35732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025848-36032.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025848-78199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025848-36810.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025848-36032.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-64571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025847-80925.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025849-21987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025849-20392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025846-92291.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025849-47779.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025849-52602.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025850-79508.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025850-58976.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025850-72531.gif)
所以,点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025850-96867.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025845-64571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025850-72531.gif)
解析
核心考点
试题【如图,抛物线(a0)与双曲线相交于点A,B. 已知点A的坐标为(1,4),点B在第三象限内,且△AOB的面积为3(O为坐标原点).(1)求实数a,b,k的值;(】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025836-39008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025836-23476.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025836-33221.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025836-53204.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025837-71646.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025837-71646.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025836-53204.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025837-88722.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025837-21792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025837-71646.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025830-75485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025830-54595.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025827-67725.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025827-54888.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025827-36510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025814-76118.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025814-19327.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025814-17691.gif)
(Ⅰ)求椭圆C的方程
(Ⅱ)过圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025814-56227.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025814-72888.gif)
①求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025815-37408.gif)
②求|AB|的取值范围
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025805-68588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025805-98990.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025805-41359.gif)
(1) 求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025805-68588.gif)
(2) 若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025806-27292.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025806-93317.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025805-68588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025806-43738.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025806-83539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025807-57452.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025807-51976.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026025807-37976.gif)
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