《高考数学（理）二轮专题突破演练（浙江专版）第3部分 专题1 第2讲“2道”拉分题专练卷2 Word版含解析.doc》由会员分享，可在线阅读，更多相关《高考数学（理）二轮专题突破演练（浙江专版）第3部分 专题1 第2讲“2道”拉分题专练卷2 Word版含解析.doc（4页珍藏版）》请在三一办公上搜索。
1、“2道”拉分题专练卷(二)1(2013温州八校联考)已知函数f(x)ex2x23x.(1)求曲线yf(x)在点(1，f(x)处的切线方程；(2)当x时，若关于x的不等式f(x)x2(a3)x1恒成立，试求实数a的取值范围解：(1)f(x)ex4x3，则f(1)e1，又f(1)e1，曲线yf(x)在点(1，f(1)处的切线方程为ye1(e1)(x1)，即(e1)xy20.(2)由f(x)x2(a3)x1，得ex2x23xx2(a3)x1，即axexx21.x，a令g(x).则g(x).令(x)ex(x1)x21，则(x)x(ex1)x，(x)0，(x)在上单调递增，(x)0，因此g(x)0，故g
2、(x)在上单调递增，则g(x)g2.a的取值范围是.2经过点F(0,1)且与直线y1相切的动圆的圆心轨迹为M.点A、D在轨迹M上，且关于y轴对称，过线段AD(两端点除外)上的任意一点作直线l，使直线l与轨迹M在点D处的切线平行，设直线l与轨迹M交于点B、C.(1)求轨迹M的方程；(2)证明：BADCAD；(3)若点D到直线AB的距离等于|AD|，且ABC的面积为20，求直线BC的方程解：(1)法一：设动圆圆心为(x，y)，依题意得，|y1|.整理，得x24y.所以轨迹M的方程为x24y.法二：设动圆圆心为P，依题意得点P到定点F(0,1)的距离和点P到定直线y1的距离相等，根据抛物线的定义可知
3、，动点P的轨迹是抛物线且其中定点F(0,1)为焦点，定直线y1为准线所以动圆圆心P的轨迹M的方程为x24y.(2)证明：由(1)得x24y，即yx2，则yx.设点D，由导数的几何意义知，直线l的斜率为kBCx0.由题意知点A，设点C，B，则kBCx0，即x1x22x0.因为kAC，kAB，所以kACkAB0，即kACkAB.所以BADCAD.(3)法一：由点D到AB的距离等于|AD|，可知BAD45.不妨设点C在AD上方，即x2x1，直线AB的方程为yx(xx0)由解得点B的坐标为.所以|AB|(x04)(x0)|2|x02|.由(2)知CADBAD45，同理可得|AC|2|x02|.所以AB
4、C的面积S2|x02|2|x02|4|x4|20，解得x03.当x03时，点B的坐标为，kBC，直线BC的方程为y(x1)，即6x4y70.待添加的隐藏文字内容2当x03时，点B的坐标为，kBC，直线BC的方程为y(x7)，即6x4y70.法二：由点D到AB的距离等于|AD|，可知BAD45.由(2)知CADBAD45，所以CAB90，即ACAB.由(2)知kAC，kAB，所以kACkAB1.即(x1x0)(x2x0)16.由(2)知，x1x22x0.不妨设点C在AD上方，即x2x1，由解得所以|AB| 2|x02|，同理，|AC|2|x02|.以下同解法一高考资源网版权所有！投稿可联系QQ：
5、108459180129C91AFE4CED1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFEDD1B6C87D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF95AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9D1B6C8795AD9C91AFE4CED1B6C8795A1AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9
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16、FFE4CED1B6C8795AD29C91AFC8795AD9C91FE4CED1B6C8795AD29C91AFD1B6C8795AD9C91AFED1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF795AD9C91FE4CED1B6C8795ADD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C9
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18、9D1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF1AFD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AFD1BD1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF1B6C8795AD9C91AFE4CED1B6C8795AD91AFE4CED1B6C8795AD9C91FE4CED1B6C8795AD29C91AF4CED1B6C8795AD29C91AFE4CED1B6C8795ADC6F554C62
