From ecbb96ac1583fc027f2bdb4c5bae5050a04ba8d5 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 14:28:04 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=89=E5=AF=92?= =?UTF-8?q?=E5=81=87=E4=BD=9C=E4=B8=9A65=E6=96=B0=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 + 题库0.3/Problems.json | 204 ++++++++++++++++++++++++++++++- 2 files changed, 203 insertions(+), 4 deletions(-) diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 724e13f3..2b95384b 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -193,3 +193,6 @@ 20240125-142435 024113:024114,012920,024115,022535,024116:024117,022570,024118 +20240125-142753 +024119:024127 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index c2a78182..f60fbffa 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -77533,7 +77533,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024124" + ], "remark": "", "space": "", "unrelated": [] @@ -320164,7 +320166,9 @@ "edit": [ "20220818\t王伟叶" ], - "same": [], + "same": [ + "024119" + ], "related": [ "000467", "000806", @@ -454611,7 +454615,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024121" + ], "remark": "", "space": "", "unrelated": [] @@ -649267,6 +649273,194 @@ "space": "4em", "unrelated": [] }, + "024119": { + "id": "024119", + "content": "抛物线 $y^2+4 x=0$ 的准线方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [ + "011456" + ], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024120": { + "id": "024120", + "content": "抛物线 $y=a x^2$ 的焦点坐标为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024121": { + "id": "024121", + "content": "抛物线以原点为顶点, 以坐标轴为对称轴, 且焦点在直线 $x-2 y-4=0$ 上, 则抛物线的标准方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "016580" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024122": { + "id": "024122", + "content": "若抛物线的顶点是原点, 焦点是椭圆 $4 x^2+y^2=1$ 的一个焦点, 则此抛物线的焦点到准线的距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024123": { + "id": "024123", + "content": "在平面直角坐标系 $x O y$ 中, 双曲线 $\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$) 的右支与焦点为 $F$ 的抛物线 $x^2=2 p y$($p>0$) 交于 $A$、$B$ 两点. 若 $AF+BF=4OF$, 则该双曲线的渐近线方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024124": { + "id": "024124", + "content": "若抛物线 $y^2=4 x$ 内有一点 $A(2,1)$, 在抛物线上找一点 $P$, 使得 $|PF|+|PA|$ 取得最小值, 则点 $P$ 的坐标为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "002402" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024125": { + "id": "024125", + "content": "已知抛物线 $C$ 的顶点是椭圆 $\\dfrac{x^2}{4}+\\dfrac{y^2}{3}=1$ 的中心, 焦点与该椭圆的右焦点 $F_2$ 重合, 若抛物线 $C$ 与该椭圆在第一象限的交点为 $P$, 椭圆的左焦点为 $F_1$, 则 $|PF_1|$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024126": { + "id": "024126", + "content": "抛物线 $y^2=4 x$ 的焦点为 $F$, 准线为 $l$, 经过点 $F$ 且斜率为 $\\sqrt{3}$ 的直线与抛物线在 $x$ 轴上方的部分相交于点 $A$, 若 $AK \\perp l$, 垂足为 $K$, 则 $\\triangle AKF$ 的面积是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024127": { + "id": "024127", + "content": "已知抛物线 $y^2=8 x$, 过动点 $M(a, 0)$ 且斜率为 $1$ 的直线 $l$ 与抛物线交于不同的两点\n$A$、$B$, 且 $|AB| \\leq 8$.\\\\\n(1) 求实数 $a$ 的取值范围;\\\\\n(2) 若线段 $AB$ 的垂直平分线交 $x$ 轴于点 $N$, 求 $\\triangle NAB$ 的面积的最大值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "040055" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0