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说明: 本系列课件,经多次使用,修改,其中有部分 来自网络,它山之石可以攻玉,希望谅解。 为了一个课件,我们仔细研磨; 为了一个习题,我们精挑细选; 为了一点进步,我们竭尽全力; 没有最好,只有更好! 制作水平有限,错误难免,请多指教: 28275061@qq.com 第十一章 坐标平面上的直线 11.2.3 直线的倾斜角和斜率 11.3.2 两条直线的位置关系 一、复习回顾: 已知两条直线方程为 l1 : a1 x ? b1 y ? c1 ? 0 l2 : a2 x ? b2 y ? c2 ? 0 ?c1 b1 ?c2 b2 , Dy ? a1 a2 ?c1 ?c2 记D ? a1 b1 a2 b2 , Dx ? Dx Dy 当 D ? 0 时,两直线相交于点 ( , ) ; D D 当 D ? Dx ? Dy ? 0 时,两直线重合; 当 D ? 0, Dx ? 0 或 Dy ? 0 时,两直线平行. 练一练 已知直线l1 : ?m ? 3?x ? 4 y ? 3m ? 5 ? 0 及直线l2 : 2 x ? ?m ? 5? y ? 8 ? 0 当 m为何值时,l1与l2 (1)相交?(2)平行? (3)重合?(4)垂直? 几个结论: (1) “ D ? 0”是“l1与l2 相交” 充要 条件. (2) “ D ? 0”是“l1与l2 平行”必要非充分 条件. (3) “ a1a2 ? b1b2 ? 0”是“l1 与l2 垂直”充要 条件. 二、综合应用 例 1.已知三条直线: 1 2 l3 : mx ? 3 y ? 5 ? 0 (1) 若三条直线有且仅有两个交点, 求 m的值; (2)若三条直线能构成一个三角形,求 m的取 值范围. l : x ? y ? 1 ? 0; l : 2 x ? y ? 8 ? 0; 练一练 当 m为何值时,三条直线 l1 : 4 x ? y ? 4; 2 3 l : mx ? y ? 0; l : 2 x ? 3my ? 4不能构成三角形? 二、综合应用 例 2. 已知直线l 的方程为 kx ? y ? 2k ? 3 ? 0, 求证:对于任意实数 k ,直线l 恒过定点 M , 并指出定点 M 的坐标. 练一练 对于任意实数 m,直线 点 . ?m ? 1?x ? ?2m ? 1? y ? 5 ? m ? 0恒过定 三、一类最值问题的解答 例 3.直线l 过点 M ?2,1?,且与 x 轴, y 轴的 正半轴分别交于 A, B 两点 9 (1)若 S ?AOB ? ,求直线l 的方程; 2 (2) 当 ?ABO 面积最小时, 求直线l 的方程; (3) 求 MA ? MB的最大值及此时直线l 的方程. y B . M(2,1) O A x 三、一类最值问题的解答 练一练 已知直线l 过点?? 2,3?, 且与 x 轴负半轴,y 轴的正半轴分别交于 A, B两点, (1)求 ?AOB的最小值时,直线的方程; (2)求截距之积最大时,直线的方程; y M(-2,3) . O x 四、课堂小结

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