收录高三寒假作业08三题

工具v2/文本文件/新题收录列表.txt

@@ -22,3 +22,6 @@
 20240124-202938
 023689:023691
 
+20240124-203157
+023692:023694
+

题库0.3/Problems.json

@@ -640094,6 +640094,66 @@
         "space": "4em",
         "unrelated": []
     },
+    "023692": {
+        "id": "023692",
+        "content": "若圆心为 $(2,-1)$ 的圆在直线 $x-y-1=0$ 上截得的弦长为 $2 \\sqrt{2}$, 则此圆方程为\\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": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023693": {
+        "id": "023693",
+        "content": "若过点 $(3,1)$ 作圆 $(x-1)^2+y^2=r^2$ 的切线有且只有一条, 则该切线的方程为\\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": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023694": {
+        "id": "023694",
+        "content": "已知以点 $C(t, \\dfrac{2}{t})$($t \\in \\mathbf{R}$, $t \\neq 0$) 为圆心的圆与 $x$ 轴交于点 $O$、$A$, 与 $y$ 轴交于点 $O$、$B$, 其中 $O$ 为坐标原点.\\\\\n(1) 求证: $\\triangle OAB$ 的面积为定值;\\\\\n(2) 设直线 $y=-2 x+4$ 与圆 $C$ 交于点 $M$、$N$, 若 $|OM|=|ON|$, 求圆 $C$ 的方程.",
+        "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.",