wangweiye
/
mathdeptv2
Archived
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

修改40504题面

This commit is contained in:
weiye.wang 2023-04-18 21:01:20 +08:00
parent d4a77df10a
commit 64dad3622f
2 changed files with 4 additions and 3 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
工具/latex界面修改题目内容.py
View File

@ -1,6 +1,6 @@
import os,re,json
"""这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭"""
problems = "40473,30499"
problems = "40504"
editor = "王伟叶"
def generate_number_set(string,dict):

5
题库0.3/Problems.json
View File

@ -470137,7 +470137,7 @@
},
"040504": {
"id": "040504",
"content": "已知直线$l: y=-\\dfrac{1}{2} x$为双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的一条渐近线, 且双曲线$C$经过点$(2 \\sqrt{2}, 1)$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.3]\n\\draw [->] (-10,0) -- (10,0) node [below] {$x$};\n\\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [dashed] (10,5) -- (-10,-5) (10,-5) -- (-10,5);\n\\draw [domain = -10:{-2*sqrt(2)}, samples = 100] plot (\\x,{sqrt(\\x*\\x/4-2)});\n\\draw [domain = -10:{-2*sqrt(2)}, samples = 100] plot (\\x,{-sqrt(\\x*\\x/4-2)});\n\\draw [domain = {2*sqrt(2)}:10, samples = 100] plot (\\x,{sqrt(\\x*\\x/4-2)});\n\\draw [domain = {2*sqrt(2)}:10, samples = 100] plot (\\x,{-sqrt(\\x*\\x/4-2)}); \n\\end{tikzpicture}\n\\end{center}\n(1) 求双曲线$C$的方程;\\\\\n(2) 设直线$l: x=t y+4$与$C$交于$M, N$, 三角形$OMN$面积为$S$, 判断: 是否存在$t$使得$S=8 \\sqrt{15}$成立? 若存在, 求出$t$的值, 否则说明理由;\\\\\n(3) 设$A, B$是双曲线右支上两点, 若直线$l$上存在点$P$, 使得$\\triangle ABP$为正三角形, 求直线$AB$的斜率的取值范围.",
"content": "已知直线$l: y=-\\dfrac{1}{2} x$为双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的一条渐近线, 且双曲线$C$经过点$(2 \\sqrt{2}, 1)$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.3]\n\\draw [->] (-10,0) -- (10,0) node [below] {$x$};\n\\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [dashed] (10,5) -- (-10,-5) (10,-5) -- (-10,5);\n\\draw [domain = -10:{-2*sqrt(2)}, samples = 100] plot (\\x,{sqrt(\\x*\\x/4-2)});\n\\draw [domain = -10:{-2*sqrt(2)}, samples = 100] plot (\\x,{-sqrt(\\x*\\x/4-2)});\n\\draw [domain = {2*sqrt(2)}:10, samples = 100] plot (\\x,{sqrt(\\x*\\x/4-2)});\n\\draw [domain = {2*sqrt(2)}:10, samples = 100] plot (\\x,{-sqrt(\\x*\\x/4-2)}); \n\\end{tikzpicture}\n\\end{center}\n(1) 求双曲线$C$的方程;\\\\\n(2) 设直线$l': x=t y+4$与$C$交于$M, N$, 三角形$OMN$面积为$S$, 判断: 是否存在$t$使得$S=8 \\sqrt{15}$成立? 若存在, 求出$t$的值, 否则说明理由;\\\\\n(3) 设$A, B$是双曲线右支上两点, 若直线$l$上存在点$P$, 使得$\\triangle ABP$为正三角形, 求直线$AB$的斜率的取值范围.",
"objs": [],
"tags": [],
"genre": "解答题",
@ -470147,7 +470147,8 @@
"usages": [],
"origin": "23届交大附中模拟卷试题20",
"edit": [
"20230401\t王伟叶"
"20230401\t王伟叶",
"20230418\t王伟叶"
],
"same": [],
"related": [],