新高考数学一轮复习精讲精练10.2 圆的方程（基础版）（原卷版）

10.2圆的方程（精讲）（基础版）思维导图思维导图考点呈现考点呈现例题剖析例题剖析考点一圆的方程【例1-1】（2021白云期末）已知圆SKIPIF1<0的方程为SKIPIF1<0，则圆心SKIPIF1<0的坐标为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例1-2】（2022成都）已知圆SKIPIF1<0的圆心在直线SKIPIF1<0上，且圆SKIPIF1<0与SKIPIF1<0轴的交点分别为SKIPIF1<0，则圆SKIPIF1<0的标准方程为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·江西模拟）设甲：实数SKIPIF1<0；乙：方程SKIPIF1<0是圆，则甲是乙的（）A．充分不必要条件 B．必要不充分条件C．充要条件 D．既不充分也不必要条件2．（2022和平）圆心在SKIPIF1<0轴上，半径为2，且过点SKIPIF1<0的圆的方程为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022杭州）过点（7，-2）且与直线SKIPIF1<0相切的半径最小的圆方程是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0考点二直线与圆的位置关系【例2-1】（2022高二下·玉溪期末）已知直线SKIPIF1<0经过点SKIPIF1<0，且SKIPIF1<0与圆SKIPIF1<0相切，则SKIPIF1<0的方程为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2022·温州）已知直线SKIPIF1<0与圆SKIPIF1<0有两个不同的交点，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-3】（2022·柳州模拟）已知直线SKIPIF1<0与圆SKIPIF1<0相交于A，B两点SKIPIF1<0，则k＝（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·秦皇岛二模）直线SKIPIF1<0被圆SKIPIF1<0截得的弦长为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·呼和浩特模拟）直线l：SKIPIF1<0与函数SKIPIF1<0的图象有两个公共点，则k的取值范围为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·贵阳模拟）已知直线SKIPIF1<0和SKIPIF1<0与圆SKIPIF1<0都相切，则圆SKIPIF1<0的面积的最大值是（）A．2π B．4π C．8π D．16π4．（2022·鞍山模拟）（多选）已知M为圆C：SKIPIF1<0上的动点，P为直线l：SKIPIF1<0上的动点，则下列结论正确的是（）A．直线l与圆C相切 B．直线l与圆C相离C．|PM|的最大值为SKIPIF1<0 D．|PM|的最小值为SKIPIF1<0考点三圆与圆的位置关系【例3-1】（2022高一下·汉中期中）已知SKIPIF1<0，SKIPIF1<0，那么它们的位置关系是（）A．外离 B．相切 C．相交 D．内含【例3-2】（2022·吉林模拟）已知两圆方程分别为SKIPIF1<0和SKIPIF1<0．则两圆的公切线有（）A．1条 B．2条 C．3条 D．4条【一隅三反】1．（2022·石家庄模拟）（多选）已知圆SKIPIF1<0与圆SKIPIF1<0，则下列说法正确的是（）A．若圆SKIPIF1<0与x轴相切，则SKIPIF1<0B．若SKIPIF1<0，则圆SKIPIF1<0与圆SKIPIF1<0相离C．若圆SKIPIF1<0与圆SKIPIF1<0有公共弦，则公共弦所在的直线方程为SKIPIF1<0D．直线SKIPIF1<0与圆SKIPIF1<0始终有两个交点2．（2022·徐汇期末）已知圆SKIPIF1<0和圆SKIPIF1<0内切，则m的值为．3（2022广安期末）若圆SKIPIF1<0平分圆SKIPIF1<0的周长，则直线SKIPIF1<0被圆SKIPIF1<0所截得的弦长为．考点四切线问题【例4-1】（2022·天津市模拟）过点SKIPIF1<0作圆SKIPIF1<0的切线SKIPIF1<0，则SKIPIF1<0的方程为（）A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<0【例4-2】（2022·湖北模拟）若圆SKIPIF1<0关于直线SKIPIF1<0对称，则从点SKIPIF1<0向圆SKIPIF1<0作切线，切线长最小值为（）A．2 B．3 C．4 D．6【一隅三反】1．（2022·朝阳模拟）过点SKIPIF1<0作圆SKIPIF1<0的切线，则切线方程为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2022·广西模拟）过圆SKIPIF1<0上一点A作圆SKIPIF1<0的切线，切点为B，则SKIPIF1<0的最小值为（）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022高二下·番禺期末）写出与圆SKIPIF1<0和圆SKIPIF1<0都相切的一条切线方程.10.2圆的方程（精练）（基础版）题组一题组一圆的方程1．（2022湖南期末）若SKIPIF1<0的三个顶点坐标分别为SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0外接圆的圆心坐标为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022成都期末）已知圆SKIPIF1<0的圆心为SKIPIF1<0，且圆SKIPIF1<0与SKIPIF1<0轴的交点分别为SKIPIF1<0，则圆SKIPIF1<0的标准方程为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022天津月考）与SKIPIF1<0轴相切，且圆心坐标为SKIPIF1<0的圆的标准方程为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·全国·高二课时练习）求满足下列条件的圆的方程，并画出图形：(1)经过点SKIPIF1<0和SKIPIF1<0，圆心在x轴上；(2)经过直线SKIPIF1<0与SKIPIF1<0的交点，圆心为点SKIPIF1<0；(3)经过SKIPIF1<0，SKIPIF1<0两点，且圆心在直线SKIPIF1<0上；(4)经过SKIPIF1<0，SKIPIF1<0，SKIPIF1<0三点．题组二直线与圆的位置关系题组二直线与圆的位置关系1（2022·滨州二模）已知直线SKIPIF1<0，圆SKIPIF1<0，则直线l与圆C的位置关系是（）A．相离 B．相切 C．相交 D．不确定2．（2022·毕节模拟）曲线SKIPIF1<0与直线SKIPIF1<0有两个交点，则实数SKIPIF1<0的取值范围为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022汕尾期末）（多选）直线SKIPIF1<0：SKIPIF1<0与圆SKIPIF1<0：SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0两点，则（）A．直线SKIPIF1<0过定点SKIPIF1<0B．SKIPIF1<0时，直线SKIPIF1<0平分圆SKIPIF1<0C．SKIPIF1<0时，SKIPIF1<0为等腰直角三角形D．SKIPIF1<0时，弦SKIPIF1<0最短4．（2022广东月考）（多选）已知点SKIPIF1<0是圆SKIPIF1<0上的任意一点，直线SKIPIF1<0，则下列结论正确的是（）A．直线SKIPIF1<0与圆SKIPIF1<0的位置关系只有相交和相切两种B．圆SKIPIF1<0的圆心到直线SKIPIF1<0距离的最大值为SKIPIF1<0C．点SKIPIF1<0到直线SKIPIF1<0距离的最小值为SKIPIF1<0D．点SKIPIF1<0可能在圆SKIPIF1<0上5．（2022盐城期末）已知直线SKIPIF1<0与圆SKIPIF1<0相切，则实数a的值为．6（2022·新高考Ⅱ卷）已知点SKIPIF1<0，若直线SKIPIF1<0关于SKIPIF1<0的对称直线与圆SKIPIF1<0存在公共点，则实数a的取值范围为．7．（2022广东）当圆SKIPIF1<0截直线SKIPIF1<0所得的弦长最短时，m的值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．-1 D．18（2022山西）．过点SKIPIF1<0的直线l与圆SKIPIF1<0有公共点，则直线l倾斜角的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09（2022山东）．过点SKIPIF1<0的直线SKIPIF1<0与圆SKIPIF1<0：SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0两点，当弦SKIPIF1<0取最大值时，直线SKIPIF1<0的方程为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0题组三题组三圆与圆的位置关系1．（2022·邯郸模拟）已知圆SKIPIF1<0：SKIPIF1<0和圆SKIPIF1<0：SKIPIF1<0，则“SKIPIF1<0”是“圆SKIPIF1<0与圆SKIPIF1<0内切”的（）A．充分不必要条件 B．必要不充分条件C．充分必要条件 D．既不充分也不必要条件2．（2022·河东模拟）圆SKIPIF1<0与圆SKIPIF1<0的公共弦长为．3．（2022·河西模拟）设SKIPIF1<0与SKIPIF1<0相交于SKIPIF1<0两点，则SKIPIF1<0．4．（2022·威海模拟）圆SKIPIF1<0与圆SKIPIF1<0的公共弦长为．5．（2022·湖南模拟）已知动圆SKIPIF1<0与圆SKIPIF1<0外切，与圆SKIPIF1<0内切，则动圆圆心SKIPIF1<0的轨迹方程为．6．（2021·山东济南市·高二期末）（多选）已知圆SKIPIF1<0和圆SKIPIF1<0的公共点为SKIPIF1<0，SKIPIF1<0，则（）A．SKIPIF1<0 B．直线SKIPIF1<0的方程是SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．（2021·全国高二课时练习）（多选）圆SKIPIF1<0和圆SKIPIF1<0的交点为A，B，则有（）A．公共弦AB所在直线方程为SKIPIF1<0B．线段AB中垂线方程为SKIPIF1<0C．公共弦AB的长为SKIPIF1<0D．P为圆SKIPIF1<0上一动点，则P到直线AB距离的最大值为SKIPIF1<08．（2022云南）已知圆SKIPIF1<0与圆SKIPIF1<0．(1)求证：圆SKIPIF1<0与圆SKIPIF1<0相交；(2)求两圆公共弦所在直线的方程；(3)求经过两圆交点，且圆心在直线SKIPIF1<0上的圆的方程．题组四题组四切线问题1．（2022哈尔滨）设圆SKIPIF1<0，圆SKIPIF1<0，则圆SKIPIF1<0，SKIPIF1<0