名校
解题方法
1 . 如图,平面直角坐标系内,
为坐标原点,点
在
轴正半轴上,点
在第一象限内,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/bb73b2c9-a8c2-47c8-9814-9dbe3fe4daac.png?resizew=157)
(1)若
过点
,且
为线段
的中点,求直线
的方程;
(2)若
,求
的面积取得最大值时直线
的方程;
(3)设
,
,若
,求证:直线
过一定点,并求出此定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1eb76fe74cba30f7cbcde349ba80da.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/bb73b2c9-a8c2-47c8-9814-9dbe3fe4daac.png?resizew=157)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f4bfd47e93f1777c88212301a09942b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0907a673d52825cd7df84b400972d4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5038ca8098994dcc635e669b6a158d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aae1bc31a8462128c1906eed27dec66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e8ddd51cf752947a523a80076bcd940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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