题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174247-92914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174247-99357.gif)
⑴如图甲,若点A在x轴正半轴上,点B在y轴正半轴上,且OA=OB.
①求k的值;
②若b=4,点P为直线
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174247-92914.gif)
⑵若
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174248-99573.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174247-92914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174248-94403.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174248-81456.jpg)
答案
(1)
①k=-1
②P的坐标为(1,3)或(3,1)
(2)b的值为
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-41100.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-91652.gif)
解析
∴A的坐标为(b,0),代入y=kx+b得k=-1.
②过P作x轴的垂线,垂足为F,连结OD.
∵PC、PD是⊙O的两条切线,∠CPD=90°,
∴∠OPD=∠OPC=
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-39747.gif)
∵∠PDO=90°,,∠POD=∠OPD=45°,
∴OD=PD=
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174247-99357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-37741.gif)
∵P在直线y=-x+4上,
设P(m,-m+4),则OF=m,PF=-m+4,
∵∠PFO=90°, OF2+PF2=PO2,
∴ m2+ (-m+4)2=(
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-37741.gif)
解得m=1或3,
∴P的坐标为(1,3)或(3,1)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174250-97820.jpg)
⑵分两种情形,y=-
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-39747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-41100.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-39747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-41100.gif)
直线
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174247-92914.gif)
如图,画出弦心距OC,可得弦心距OC=
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174250-24669.gif)
又∵直线
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174247-92914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174248-99573.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-39747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174250-27734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174247-99357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174250-58934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174250-58934.gif)
所以直线与y轴交于点(
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-41100.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-41100.gif)
当直线与x轴、y轴的负半轴相交,同理可求得b的值为
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-91652.gif)
综合以上得:b的值为
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-41100.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174249-91652.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174251-81610.jpg)
核心考点
试题【在平面直角坐标系中,直线(k为常数且k≠0)分别交x轴、y轴于点A、B,⊙O半径为个单位长度.⑴如图甲,若点A在x轴正半轴上,点B在y轴正半轴上,且OA=OB.】;主要考察你对平面直角坐标系等知识点的理解。[详细]
举一反三
若点
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174238-38237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174239-47550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174239-71744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174239-73111.png)
A.第一、二、三象限 | B.第一、二、四象限 |
C.第二、三、四象限 | D.第一、三、四象限 |
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174229-93645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174229-37880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174230-48457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174230-69399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174230-67058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174230-79108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174230-67058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174230-79108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174223-43914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174224-16144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174224-15120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174225-98363.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174215-64806.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174215-98676.gif)
(1)画出△
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174215-64806.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174216-55442.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174216-49035.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174216-49035.gif)
(2)把(1)中的△
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174216-49035.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174216-84635.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174216-19548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174217-77861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174217-77861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174217-77861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191119/20191119174215-64806.gif)
A.(-1,-3) | B.(2,1) | C.(-2,1) | D.(1,-2) |
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