高中数学训练题及解析——直线与圆的位置关系.doc

平面解析几何直线与圆的位置关系一、选择题1已知直线l过点(2,0)，当直线l与圆x2y22x有两个交点时，其斜率k的取值范围是()A(2，2)B(，)C(，) D(，)答案C解析设l的方程yk(x2)，即kxy2k0.圆心为(1,0)由已知有1，k.2直线xsinycos2sin与圆(x1)2y24的位置关系是()A相离 B相切C相交 D以上都有可能答案B解析圆心到直线的距离d2.所以直线与圆相切3平移直线xy10使其与圆(x2)2(y1)21相切，则平移的最短距离为()A.1 B2C. D.1与1答案A解析如图，圆心(2,1)到直线l0：xy10的距离d，圆的半径为1，故直线l0与l1的距离为1，平移的最短距离为1，故选A.4已知圆O1：(xa)2(yb)24；O2：(xa1)2(yb2)21(a，bR)，那么两圆的位置关系是()A内含 B内切C相交 D外切答案C解析由两圆方程易知其圆心坐标分别为O1(a，b)、O2(a1，b2)，经计算得：O1O2，由于Rr1O1O2Rr3，故两圆相交5函数yf(x)的图象是圆心在原点的单位圆在、象限内的两段圆孤，如图，则不等式f(x)213，两圆相离把所给的轨迹方程化简得4x3y70显然线段O1O2的中点不在直线4x3y70上，排除A、C，由计算知，到两圆的切线长相等的点的轨迹恰为直线4x3y70.8已知圆C：x2y21，点A(2,0)及点B(2，a)，从A点观察B点，要使视线不被圆C挡住，则a的取值范围是()A(，1)(1，)B(，2)(2，)C(，)(，)D(，4)(4，)答案C解析解法一：(直接法)写出直线方程，将直线与圆相切转化为点到直线的距离来解决过A、B两点的直线方程为yx，即ax4y2a0，则d1，化简后，得3a216，解得a.再进一步判断便可得到正确答案为C.解法二：设AB1直线方程为(1k2)x24k2x4k210，0，k，直线AB1方程为y(x2)，直线AB2方程为y(x2)，可得B1(2，)，B2(2，)，要使从A看B不被圆挡住，B纵坐标即实数a的取值范围为(，)(，)9若圆(x3)2(y5)2r2上有且只有两个点到直线4x3y20的距离等于1，则半径r的取值范围是()A(4,6) B4,6)C(4,6 D4,6答案A二、填空题10已知直线xya与圆x2y24交于A，B两点，且|(其中O为坐标原点)，则实数a等于_答案2解析由|知OAOB，所以由题意可得，所以a2.11过点M(1,2)的直线l将圆(x2)2y29分成两段弧，其中的劣弧最短时，直线l的方程为_答案x2y30解析设圆心为N(2,0)，由圆的性质得直线lMN时，形成的劣弧最短，由点斜式得直线l的方程为x2y30.12(2010江西卷，理)直线ykx3与圆(x3)2(y2)24相交于M，N两点，若|MN|2，则k的取值范围是_答案，0解析如图，记题中圆的圆心为C(3,2)，作CDMN于D，则|CD|，于是有|MN|2|MD|222，即43，解得k0.13若直线yxb与曲线x恰有一个公共点，则b取值范围是_答案1b1或b解析xx2y21(x0)方程x2y21(x0)所表示的曲线为半圆(如图)当直线与圆相切时或在l2与l3之间时，适合题意三、解答题14已知圆C：x2y22x4y30.若圆C的切线在x轴和y轴上的截距的绝对值相等，求此切线的方程解析切线在两坐标轴上截距的绝对值相等，切线的斜率是1.设切线方程为yxb或yxc，分别代入圆C的方程得2x22(b3)x(b24b3)0或2x22(c1)x(c24c3)0，由于相切，则方程有等根，即b3或b1，c5或c1.故所求切线方程为：xy30，xy10，xy50，xy10.15(2011北京海淀区期末)已知圆C经过点A(2,0)，B(0,2)，且圆心C在直线yx上，又直线l：ykx1与圆C相交于P、Q两点(1)求圆C的方程；(2)若2，求实数k的值；(3)过点(0,1)作直线l1与l垂直，且直线l1与圆C交于M、N两点，求四边形PMQN面积的最大值解设圆心C(a，a)，半径为r.因为圆C经过点A(2,0)，B(0,2)，所以|AC|BC|r，易得a0，r2，所以圆C的方程是x2y24.(2)因为22cos，2，且与的夹角为POQ，所以cosPOQ，POQ120，所以圆心到直线l：kxy10的距离d1，又d，所以k0.(3)设圆心O到直线l，l1的距离分别为d，d1，四边形PMQN的面积为S.因为直线l，l1都经过点(0,1)，且ll1，根据勾股定理，有dd21.又易知|PQ|2，|MN|2，所以S|PQ|MN|，即S22222 2 7，当且仅当d1d时，等号成立，所以S的最大值为7.技术官员村位于位于亚运城东部，主干道二以东石楼涌以西的地块，占地面积、m2，总建筑面积、m2，共包括地下室南区、地下室北区、地上部分1栋12栋、服务中心、室外工程等多个单体工程。其中住宅面积m2，共12栋，17栋建筑层数为11层，812栋11层（局部复式顶层），首层局部架空，布置公建配套设施。integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed,