收录高三寒假作业07三题

工具v2/文本文件/新题收录列表.txt

@@ -19,3 +19,6 @@
 20240124-202600
 023683:023688
 
+20240124-202938
+023689:023691
+

题库0.3/Problems.json

@@ -74527,7 +74527,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023690"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -255937,7 +255939,9 @@
         "edit": [
             "20220726\t王伟叶"
         ],
-        "same": [],
+        "same": [
+            "023689"
+        ],
         "related": [],
         "remark": "",
         "space": "",
@@ -640026,6 +640030,70 @@
         "space": "4em",
         "unrelated": []
     },
+    "023689": {
+        "id": "023689",
+        "content": "若圆 $C: x^2+y^2+k x+2 y=-k^2$($k \\in \\mathbf{R}$), 则当圆 $C$ 面积最大时, 圆心 $C$ 的坐标为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [
+            "009076"
+        ],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023690": {
+        "id": "023690",
+        "content": "若实数 $x$、$y$ 满足 $x^2+y^2-4 x+1=0$, 则 $x-y$ 的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "002292"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023691": {
+        "id": "023691",
+        "content": "在平面直角坐标系 $x O y$ 中, 曲线 $\\Gamma: y=x^2-m x+2 m$($m \\in \\mathbf{R}$) 与 $x$ 轴交于不同的两点\n$A$、$B$, 曲线 $\\Gamma$ 与 $y$ 轴交于点 $C$.\\\\\n(1) 是否存在以 $AB$ 为直径的圆过点 $C$ ? 若存在, 求出该圆的方程; 若不存在, 请说明理由;\\\\\n(2) 求证: 过 $A$、$B$、$C$ 三点的圆过定点.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",