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收录高二下学期周末卷03新题

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3
工具v2/文本文件/新题收录列表.txt
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@ -391,3 +391,6 @@
20240304-143411
024621
20240304-162932 高二下学期周末卷03
040965,041052:041058,002376,041059:041060,016660,041061:041062,021253,041063:041064

341
题库0.3/Problems.json
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"content": "一条渐近线方程为 $2 x-3 y=0$ 、焦距为 6 的双曲线标准方程为\\blank{50}; 渐近线互相垂直,且 $a^2=c$ 的双曲线标准方程为\\blank{50}.",
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"content": "双曲线 $4 x^2-y^2=8$ 的两条渐近线所成的锐角是\\blank{50}; 若一双曲线的两渐近线的夹角为 $60^{\\circ}$, 实轴长为 4 , 则焦距为\\blank{50}.",
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"content": "已知一动圆 $P$ 与两定圆 $O_1:(x+4)^2+y^2=1$, $O_2: x^2+y^2-8 x+7=0$ 均内切, 那么动圆 $P$ 的圆心轨迹是\\blank{50}.",
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"041063": {
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"content": "动点 $M$ 到两定点 $(a, 0)$, $(-a, 0)$ 连线的斜率之积为 $k$, 求动点 $M$ 的轨迹, 并讨论当 $k$ 值在实数域 $R$ 内变化时曲线的变化情况.",
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"content": "已知两定点 $F_1(-\\sqrt{2}, 0), F_2(\\sqrt{2}, 0)$, 满足条件 $|\\overrightarrow{PF_2}|-|\\overrightarrow{PF_1}|=2$ 的点 $P$ 的轨迹是曲线 $E$, 直线 $y=k x-1$ 与曲线 $E$ 交于 $A, B$ 两点.如果 $|AB|=6 \\sqrt{3}$, 且曲线 $E$ 上存在点 $C$, 使 $\\overrightarrow{OA}+\\overrightarrow{OB}=m \\overrightarrow{OC}$. 求 $m$ 的值和 $\\triangle ABC$ 的面积 $S$.",
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