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2008 届二轮专题复习:解析几何题型与方法(文科) 一、考点回顾 1.直线 (1).直线的倾斜角和斜率 (2) .直线的方程 a.点斜式: y ? y1 ? k(x ? x1) ; b.截距式: y ? kx ? b ; c.两点式: y ? y1 ? x ? x1 ; d.截距式: x ? y ? 1 ; y2 ? y1 x2 ? x1 ab e.一般式: Ax ? By ? C ? 0 ,其中 A、B 不同时为 0. (3).两直线的位置关系 两条直线 l1 ,l2 有三种位置关系:平行(没有公共点);相交(有且只有一个公共点);重 合(有无数个公共点).在这三种位置关系中,我们重点研究平行与相交. (4).简单的线性规划. ①存在一定的限制条件,这些约束条件如果由 x、y 的一次不等式(或方程)组成的不等式 组来表示,称为线性约束条件. ②都有一个目标要求,就是要求依赖于 x、y 的某个函数(称为目标函数)达到最大值或最 小值.特殊地,若此函数是 x、y 的一次解析式,就称为线性目标函数. ③求线性目标函数在线性约束条件下的最大值或最小值问题,统称为线性规划问题. 2. 圆 (1).圆的定义 (2).圆的方程 a.圆的标准方程,b.圆的一般方程, c.圆的参数方程 (3).直线与圆 3.圆锥曲线 (1).椭圆的性质 条件 {M|MF1|+|MF2|=2a , 2a >|F1F2|} | MF1| {M| 点M到l1的距离 = | MF2 | 点M到l2 的距离 = e,0<e<1} 标准方程 顶点 轴 焦点 焦距 x2 ? y2 ? 1(a>b>0) a2 b2 x2 ? y2 ? 1(a>b>0) b2 a2 A1(- a , 0), A2(a , 0) B1(0 ,- b), B2(0 , b) A1(0 ,- a), A2(0 , a) B1(- b , 0), B2(b , 0) 对称轴: x 轴, y 轴.长轴长|A1A2|=2a ,短轴长|B1B2|=2b F1(- c , 0), F2(c , 0) F1(0 ,- c), F2(0 , c) |F1F2|=2c(c > 0), c2=a2 - b2 离心率 e= c (0<e<1) a 准线方程 l1 :x= ? a2 c ;l2 :x= a2 c 焦点半径 |MF1|= a + ex0 , |MF2|= a - ex0 > l1 :y= ? a2 c ;l2 :y= a2 c |MF1|= a + ey0 , |MF2|= a - ey0 外 点和椭圆 的关系 x 2 0 a2 ? y 2 0 b2 ? 1 ? (x0 , y0 )在椭圆上 < 内 (k 为切线斜率), y=kx± a 2 k 2 ? b 2 (k 为切线斜率), y=kx± b 2 k 2 ? a 2 切线方程 x 0 x + y0 y =1 a2 b2 x 0 x + y0 y =1 b2 a2 切点弦 方 程 (x0 , y0)为切点 (xx00x,+y0y)在0 y椭=圆1 外 a2 b2 (x0 , y0)为切点 (xx00x,+y0y)0在y 椭=圆1 外 b2 a2 | x2 -x1| 1 + k 2 或| y1-y2 | 1+ 1 k2 弦长公式 其中(x1 , y1),(x2 , y2)为割弦端点坐标, k 为割弦所在直 线的斜率 (2)双曲线的性质 切点弦 方程 (x0 , y0)在双曲线外 x 0 x - y 0 y =1 a2 b2 (x0 , y0)在双曲线外 y 0 y - x 0 x =1 a2 b2 弦长公式 | x 2 -x1| 1 + k 2 或| y1-y 2 | 1+ 1 k2 其中(x1 , y1),(x2 , y2)为割弦端点坐标, k 为 割弦所在直线的斜率 条件 标准方程 顶点 轴 焦点 焦距 离心率 准线方程 P ={M|MF1|-|MF2|= 2a , a > 0 , 2a <|F1F2|}. P={M| | MF1 | 点M到l1的距离 = |MF2 | 点M到l2 的距离 =e,e>1}. x2 - y2 =1(a>0,b>0) a2 b2 y2 - x2 =1(a>0,b>0) a2 b2 A1(- a , 0), A2(a , 0) A1(0 ,- a), A2(0 , a) 对称轴: x 轴, y 轴,实轴长|A1A2|= 2a ,虚轴长|B1B2|= 2b F1(- c , 0), F2(c , 0) F1(0 ,- c), F2(0 , c) |F1F2|= 2c(c > 0), c2 = a2 + b2 e= c (e>1) a l1 :x=- a2 c ;l2 :x= a2 c l1 :y=- a2 c ;l2 :y= a2 c 渐近线 y=± b x(或 x2 - y2 =0) y=± a x(或 y2 - x2 =0) 方程 a a2 b2 b a2 b2 共渐近线 的双曲线 系方程 焦点半径 x2 - y2 =k(k≠0) a2 b2 |MF1|= ex0 + a , |yM=F2k|x=±ex0a - 2k 2a ? b2 y2 - x2 =k(k≠0) a2 b2 |MF1|= ey0 + a , |yM=F2k|x=±ey0b-2 k 2a ? a 2 切线方程 (k 为切线斜率) k> b 或k<- b x0x a - y0y a =1 a2 b2 (k 为切线斜率) k> a 或k<- a y0y b - x0x b =1 a2 b2 ((x0 , y0)为切点 ((x0 , y0)为切点

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