名校
解题方法
1 . 已知抛物线
,过点
作不与x轴垂直的直线
,
分别与抛物线C交于M,N和P、Q两点.
(1)若M,N两点的纵坐标之和为-6,求直线l的斜率;
(2)证明:
;
(3)若点E为线段MN的中点,点G为线段PQ的中点,求
的值.
注:k表示直线的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53efcba08b1c0c9f7b495c2a289ebea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
(1)若M,N两点的纵坐标之和为-6,求直线l的斜率;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c719342ee48eb3c22ae4c78f5e325e.png)
(3)若点E为线段MN的中点,点G为线段PQ的中点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0465c3a283ffcf2b26097c9a8e3d380.png)
注:k表示直线的斜率.
您最近一年使用:0次
2023-05-20更新
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2卷引用:重庆市第八中学校2023-2024学年高二下学期入学适应性训练数学试题
2 . 圆锥曲线C的弦AB与过弦的端点A,B的两条切线的交点P所围成的三角形PAB叫做阿基米德三角形,若曲线C的方程为
,弦AB过C的焦点F,设
,
,
,则有
,
,对于C的阿基米德三角形PAB给出下列结论:①点P在直线
上;②
;③
;④
,其中所有正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c45b5bbd5fb7706c6f7c24df34fc145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e393f5e77659df4bc874f0009c717c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c25a40d4669c43aff783e59de769b6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39978841bdbe3d4d968557f8048f223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2781fb4bd9c996d2aba684886e1634e2.png)
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2023-02-08更新
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5卷引用:重庆市缙云教育联盟2023-2024学年高二下学期2月月度质量检测数学试题