录入W20260602新题

题库0.3/Problems.json

@@ -734565,6 +734565,46 @@
         "space": "4em",
         "unrelated": []
     },
+    "032097": {
+        "id": "032097",
+        "content": "已知三个互不相同的实数 $a$、$b$、$c$ 满足 $a+b+c=1$, $a^2+b^2+c^2=3$, 则 $a b c$ 的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240228\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "032098": {
+        "id": "032098",
+        "content": "已知椭圆 $\\Gamma$ 的离心率是 $\\dfrac{1}{2}$, 长轴长 $4$, 椭圆的中心是坐标原点, 焦点在 $x$ 轴上.\n    \\begin{center}\n    \\begin{tikzpicture}[>=latex]\n    \\draw [->] (-2.5,0) -- (2.5,0) node [below] {$x$};\n    \\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n    \\draw (0,0) node [below left] {$O$};\n    \\draw (0,0) ellipse (2 and {sqrt(3)});\n    \\filldraw (-1,0) circle (0.03) (1,0) circle (0.03) node [below] {$F$};\n    \\end{tikzpicture}\n    \\end{center}\n    (1) 求椭圆 $\\Gamma$ 的标准方程;\\\\\n    (2) 已知 $A, B, C$ 是椭圆 $\\Gamma$ 上三个不同的点, $F$ 是椭圆 $\\Gamma$ 的右焦点, 若原点 $O$ 是 $\\triangle ABC$ 的重心, 求 $|FA|+|FB|+|FC|$ 的值;\\\\\n    (3) 已知 $T(1,1)$, 椭圆 $\\Gamma$ 四个动点 $M, N, P, Q$ 满足 $\\overrightarrow{MT}=3 \\overrightarrow{TQ}$, $\\overrightarrow{NT}=3 \\overrightarrow{TP}$,求直线 $MN$ 的方程.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240228\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "040001": {
         "id": "040001",
         "content": "参数方程$\\begin{cases}x=3 t^2+4, \\\\ y=t^2-2\\end{cases}$($0 \\leq t \\leq 3$)所表示的曲线是\\bracket{20}.\n\\fourch{一支双曲线}{线段}{圆弧}{射线}",