收录高三寒假作业67新题

工具v2/文本文件/新题收录列表.txt

@@ -199,3 +199,6 @@
 20240125-143125
 021294,024128:024129,013757,024130:024132
 
+20240125-143409
+031229,024133:024135,016576,024136
+

题库0.3/Problems.json

@@ -299226,7 +299226,9 @@
             "20220806\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024134"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -570514,7 +570516,9 @@
             "20230101\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024135"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -649561,6 +649565,90 @@
         "space": "4em",
         "unrelated": []
     },
+    "024133": {
+        "id": "024133",
+        "content": "若 $a>1$, 则双曲线 $\\dfrac{x^2}{a^2}-y^2=1$ 的离心率的取值范围是\\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": []
+    },
+    "024134": {
+        "id": "024134",
+        "content": "若椭圆 $C: \\dfrac{x^2}{2}+y^2=1$, 直线 $l: y=x+3$, 则椭圆 $C$ 上的点到直线 $l$ 距离最大值为\\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": [
+            "010702"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024135": {
+        "id": "024135",
+        "content": "椭圆 $\\dfrac{x^2}{9}+\\dfrac{y^2}{4}=1$ 的焦点为 $F_1$、$F_2$, 点 $P$ 为椭圆上一动点, 当 $\\angle F_1PF_2$ 为钝角时, 点 $P$ 的横坐标的取值范围是\\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": [
+            "021201"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024136": {
+        "id": "024136",
+        "content": "椭圆 $C_1: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$) 的焦点 $F_1$、$F_2$ 是等轴双曲线 $C_2: \\dfrac{x^2}{2}-\\dfrac{y^2}{2}=1$ 的顶点, 若椭圆 $C_1$ 与双曲线 $C_2$ 的一个交点是 $P, \\triangle PF_1F_2$ 的周长为 $4+2 \\sqrt{2}$.\\\\\n(1) 求椭圆 $C_1$ 的标准方程;\\\\\n(2) 点 $M$ 是双曲线 $C_2$ 上任意不同于其顶点的动点, 设直线 $MF_1$、$MF_2$ 的斜率分别为 $k_1$、$k_2$, 求证: $k_1$、$k_2$ 的乘积为定值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "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.",