题目
题型:广东省高考真题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183228-45453.gif)
(1)过点A(p0,
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183229-80672.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183229-93213.gif)
(2)设M(a,b)是定点,其中a,b满足a2-4b>0,a≠0。过M(a,b)作L的两条切线l1,l2,切点分别为E(p1,
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183229-89512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183229-89512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183229-16334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183229-16334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183230-55359.gif)
(3)设D={(x,y)|y≤x-1,y≥
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183230-71513.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183230-39932.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183230-66987.gif)
直线AB方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183230-96010.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183231-97992.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183231-22149.gif)
方程
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183231-57167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183231-40220.gif)
两根
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183232-27786.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183232-25461.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183232-81606.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183232-64665.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183233-20457.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183233-35927.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183233-96979.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183234-41940.gif)
(2)由
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183234-59561.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183234-77151.gif)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183234-87313.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183234-30662.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183235-68501.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183235-88995.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183235-77748.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183235-58648.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183236-95110.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183236-23201.gif)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183236-39320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183236-88323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183236-12714.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183237-45655.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183237-43683.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183237-74228.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183237-75588.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183238-10670.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183238-70238.gif)
根据曲线的对称性可知,当
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183238-73580.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183238-22819.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183238-27405.gif)
综上所述
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183239-13801.gif)
由(1)知点M在直线EF上,方程
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183239-40605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183239-42866.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183239-85407.gif)
同理点M在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183240-95271.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183240-53324.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183240-21335.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183240-92250.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183241-85264.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183241-70896.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183241-69401.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183241-72578.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183241-91559.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183242-37903.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183242-61573.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183242-69307.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183242-86551.gif)
又由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183243-56683.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183243-82509.gif)
综合(*)式,得证。
(3)联立
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183243-25872.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183243-45007.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183244-85223.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183244-61528.gif)
过点作抛物线L的切线,设切点为
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183244-78691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183244-59451.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183244-37116.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183245-79361.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183245-29690.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183245-10697.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183245-92180.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183246-47095.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183246-14498.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183246-32786.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183246-79962.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183246-89906.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183247-28057.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183247-33287.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183247-11241.gif)
核心考点
试题【在平面直角坐标系xOy上,给定抛物线L:y=x2,实数p,q满足p2-4q≥0,x1,x2是方程x2-px+q=0的两根,记φ(p,q)=max{|x1|,|x】;主要考察你对一元二次不等式的解法等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183219-88459.gif)
(1)求α、β的值;
(2)证明:对任意的正整数n,都有an>α;
(3)记bn=ln
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183220-34419.gif)
(1)求a1;
(2)求数列{an}的通项公式;
(3)设bn=
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183100-52294.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183100-64251.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183055-71345.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183055-78245.gif)
A.(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183056-16051.gif)
B.[
![](http://img.shitiku.com.cn/uploads/allimg/20191016/20191016183056-14739.gif)
C.[3,+∞)
D.(0,3]
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