收录高三寒假作业66新题

工具v2/文本文件/新题收录列表.txt

@@ -196,3 +196,6 @@
 20240125-142753
 024119:024127
 
+20240125-143125
+021294,024128:024129,013757,024130:024132
+

题库0.3/Problems.json

@@ -649461,6 +649461,106 @@
         "space": "4em",
         "unrelated": []
     },
+    "024128": {
+        "id": "024128",
+        "content": "设 $O$ 为坐标原点, 若抛物线 $y^2=2 x$ 与过焦点的直线交于点 $A$、$B$, 则 $\\overrightarrow{OA}\\cdot \\overrightarrow{OB}=$\\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": []
+    },
+    "024129": {
+        "id": "024129",
+        "content": "设 $F$ 为抛物线 $y^2=4 x$ 的焦点, $A$、$B$、$C$ 为该抛物线上三点, 若 $A$、$B$、$C$ 三点坐标分别为 $(1,2)$、$(x_1, y_1)$、$(x_2, y_2)$, 且 $|\\overrightarrow{FA}|+|\\overrightarrow{FB}|+|\\overrightarrow{FC}|=10$, 则 $x_1+x_2=$\\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": []
+    },
+    "024130": {
+        "id": "024130",
+        "content": "已知点 $P$ 是抛物线 $y^2=2 x$ 上动点, $A(\\dfrac{7}{2}, 4)$, 若点 $P$ 到 $y$ 轴的距离为 $d_1$, 点 $P$ 到点 $A$ 的距离为 $d_2$, 则 $d_1+d_2$ 的最小值是\\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": []
+    },
+    "024131": {
+        "id": "024131",
+        "content": "已知 $F$ 为抛物线 $C: y^2=6 x$ 的焦点, 过点 $F$ 的直线 $l$ 与抛物线 $C$ 相交于 $A$、$B$ 两点, 若 $|AF|=3|BF|$, 则 $|AB|$ 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": []
+    },
+    "024132": {
+        "id": "024132",
+        "content": "已知抛物线 $C: y^2=2 x$, 点 $A(2,0)$、$B(-2,0)$, 过点 $A$ 的直线 $l$ 与抛物线 $C$ 交于 $M$、$N$两点. 求证: $\\angle ABM=\\angle ABN$.",
+        "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.",