高考數(shù)學(xué)二輪復(fù)習(xí)核心專題講練：解析幾何第1講 直線與圓綜合問題原卷版

第1講直線與圓綜合問題目錄第一部分：知識強(qiáng)化第二部分：重難點(diǎn)題型突破突破一：直線傾斜角與斜率突破二：兩條直線平行與垂直突破三：直線方程突破四：距離問題突破五：圓的方程突破六：與圓上點(diǎn)有關(guān)的距離最值問題突破七：圓的切線問題突破八：兩圓的公共弦問題突破九：圓的弦長問題第三部分：沖刺重難點(diǎn)特訓(xùn)第一部分：知識強(qiáng)化1、直線斜率的坐標(biāo)公式如果直線經(jīng)過兩點(diǎn)SKIPIF1<0，SKIPIF1<0（SKIPIF1<0），那么可得到如下斜率公式：SKIPIF1<0（1）當(dāng)SKIPIF1<0時(shí)，直線與SKIPIF1<0軸垂直，直線的傾斜角SKIPIF1<0，斜率不存在；（2）斜率公式與兩點(diǎn)坐標(biāo)的順序無關(guān)，橫縱坐標(biāo)的次序可以同時(shí)調(diào)換；（3）當(dāng)SKIPIF1<0時(shí)，斜率SKIPIF1<0，直線的傾斜角SKIPIF1<0，直線與SKIPIF1<0軸重合或者平行。2、兩條不重合直線平行的判定的一般結(jié)論是：SKIPIF1<0或SKIPIF1<0，SKIPIF1<0斜率都不存在.3、兩條直線垂直的一般結(jié)論為：SKIPIF1<0或一條直線的斜率不存在，同時(shí)另一條直線的斜率等于零．4、直線方程①直線SKIPIF1<0過點(diǎn)SKIPIF1<0和斜率SKIPIF1<0（已知一點(diǎn)+斜率）：SKIPIF1<0②直線SKIPIF1<0的斜率為SKIPIF1<0且在SKIPIF1<0軸上的縱截距為SKIPIF1<0（已知斜率+縱截距）：SKIPIF1<0③直線SKIPIF1<0在SKIPIF1<0軸上的截距為SKIPIF1<0，在SKIPIF1<0軸上的截距為SKIPIF1<0：SKIPIF1<0④直線的一般式方程：SKIPIF1<05、直線系方程（1）平行直線系方程把平面內(nèi)具有相同方向的直線的全體稱為平行直線系.一般地，與直線SKIPIF1<0平行的直線系方程都可表示為SKIPIF1<0(其中SKIPIF1<0為參數(shù)且SKIPIF1<0≠C)，然后依據(jù)題設(shè)中另一個(gè)條件來確定SKIPIF1<0的值.（2）垂直直線系方程一般地，與直線SKIPIF1<0垂直的直線系方程都可表示為SKIPIF1<0(其中SKIPIF1<0為參數(shù)），然后依據(jù)題設(shè)中的另一個(gè)條件來確定SKIPIF1<0的值.6、點(diǎn)到直線的距離平面上任意一點(diǎn)SKIPIF1<0到直線SKIPIF1<0：SKIPIF1<0的距離SKIPIF1<0.7、對稱問題（1）點(diǎn)關(guān)于點(diǎn)對稱問題(方法：中點(diǎn)坐標(biāo)公式)求點(diǎn)SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0的對稱點(diǎn)SKIPIF1<0由：SKIPIF1<0SKIPIF1<0SKIPIF1<0（2）點(diǎn)關(guān)于直線對稱問題（聯(lián)立兩個(gè)方程）求點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0：SKIPIF1<0的對稱點(diǎn)SKIPIF1<0①設(shè)SKIPIF1<0中點(diǎn)為SKIPIF1<0利用中點(diǎn)坐標(biāo)公式得SKIPIF1<0，將SKIPIF1<0代入直線SKIPIF1<0：SKIPIF1<0中；②SKIPIF1<0整理得：SKIPIF1<0（3）直線關(guān)于點(diǎn)對稱問題(求SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0的對稱直線SKIPIF1<0，則SKIPIF1<0）方法一：在直線SKIPIF1<0上找一點(diǎn)SKIPIF1<0，求點(diǎn)SKIPIF1<0關(guān)于點(diǎn)SKIPIF1<0對稱的點(diǎn)SKIPIF1<0，根據(jù)SKIPIF1<0，再由點(diǎn)斜式求解；方法二：由SKIPIF1<0SKIPIF1<0，設(shè)出SKIPIF1<0的直線方程，由點(diǎn)SKIPIF1<0到兩直線的距離相等SKIPIF1<0求參數(shù).方法三：在直線SKIPIF1<0任意一點(diǎn)SKIPIF1<0，求該點(diǎn)關(guān)于點(diǎn)SKIPIF1<0對稱的點(diǎn)SKIPIF1<0，則該點(diǎn)SKIPIF1<0在直線SKIPIF1<0上.（4）直線關(guān)于直線對稱問題4.1直線SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）和SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）相交,求SKIPIF1<0關(guān)于直線SKIPIF1<0的對稱直線SKIPIF1<0①求出SKIPIF1<0與SKIPIF1<0的交點(diǎn)SKIPIF1<0②在SKIPIF1<0上任意取一點(diǎn)SKIPIF1<0(非SKIPIF1<0點(diǎn)），求出SKIPIF1<0關(guān)于直線SKIPIF1<0的對稱點(diǎn)SKIPIF1<0③根據(jù)SKIPIF1<0，SKIPIF1<0兩點(diǎn)求出直線SKIPIF1<04.2直線SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）和SKIPIF1<0：SKIPIF1<0（SKIPIF1<0）平行,求SKIPIF1<0關(guān)于直線SKIPIF1<0的對稱直線SKIPIF1<0①SKIPIF1<0②在直線SKIPIF1<0上任取一點(diǎn)SKIPIF1<0，求點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0的對稱點(diǎn)SKIPIF1<0，利用點(diǎn)斜式求直線SKIPIF1<0.8、圓的標(biāo)準(zhǔn)方程我們把方程SKIPIF1<0稱為圓心為SKIPIF1<0半徑為SKIPIF1<0的圓的標(biāo)準(zhǔn)方程.9、圓上的點(diǎn)到定點(diǎn)的最大、最小距離設(shè)SKIPIF1<0的方程SKIPIF1<0，圓心SKIPIF1<0，點(diǎn)SKIPIF1<0是SKIPIF1<0上的動(dòng)點(diǎn)，點(diǎn)SKIPIF1<0為平面內(nèi)一點(diǎn)；記SKIPIF1<0;①若點(diǎn)SKIPIF1<0在SKIPIF1<0外，則SKIPIF1<0;SKIPIF1<0②若點(diǎn)SKIPIF1<0在SKIPIF1<0上，則SKIPIF1<0;SKIPIF1<0③若點(diǎn)SKIPIF1<0在SKIPIF1<0內(nèi)，則SKIPIF1<0;SKIPIF1<010、圓的一般方程對于方程SKIPIF1<0（SKIPIF1<0為常數(shù)），當(dāng)SKIPIF1<0時(shí)，方程SKIPIF1<0叫做圓的一般方程.①當(dāng)SKIPIF1<0時(shí)，方程表示以SKIPIF1<0為圓心，以SKIPIF1<0為半徑的圓；②當(dāng)SKIPIF1<0時(shí)，方程表示一個(gè)點(diǎn)SKIPIF1<0③當(dāng)SKIPIF1<0時(shí)，方程不表示任何圖形說明：圓的一般式方程特點(diǎn)：①SKIPIF1<0和SKIPIF1<0前系數(shù)相等（注意相等，不一定要是1）且不為0；②沒有SKIPIF1<0項(xiàng)；③SKIPIF1<0.11、直線與圓相交記直線SKIPIF1<0被圓SKIPIF1<0截得的弦長為SKIPIF1<0的常用方法（1）幾何法（優(yōu)先推薦）①弦心距（圓心到直線的距離）②弦長公式：SKIPIF1<0（2）代數(shù)法直線SKIPIF1<0：SKIPIF1<0；圓SKIPIF1<0SKIPIF1<0聯(lián)立SKIPIF1<0消去“SKIPIF1<0”得到關(guān)于“SKIPIF1<0”的一元二次函數(shù)SKIPIF1<0弦長公式：SKIPIF1<012、圓上點(diǎn)到直線的最大（?。┚嚯x設(shè)圓心到直線的距離為SKIPIF1<0，圓的半徑為SKIPIF1<0①當(dāng)直線與圓相離時(shí)，圓上的點(diǎn)到直線的最大距離為：SKIPIF1<0，最小距離為：SKIPIF1<0；②當(dāng)直線與圓相切時(shí)，圓上的點(diǎn)到直線的最大距離為：SKIPIF1<0，最小距離為：SKIPIF1<0；③當(dāng)直線與圓相交時(shí)，圓上的點(diǎn)到直線的最大距離為：SKIPIF1<0，最小距離為：SKIPIF1<0；13、圓與圓的公共弦（1）圓與圓的公共弦圓與圓相交得到的兩個(gè)交點(diǎn)，這兩點(diǎn)之間的線段就是兩圓的公共弦.（2）公共弦所在直線的方程設(shè)SKIPIF1<0:SKIPIF1<0SKIPIF1<0:SKIPIF1<0聯(lián)立作差得到：SKIPIF1<0即為兩圓共線方程（3）公共弦長的求法代數(shù)法：將兩圓的方程聯(lián)立，解出兩交點(diǎn)的坐標(biāo)，利用兩點(diǎn)間的距離公式求其長．幾何法：求出公共弦所在直線的方程，利用勾股定理解直角三角形，求出弦長．第二部分：重難點(diǎn)題型突破突破一：直線傾斜角與斜率1．（2022·湖南·懷化市湖天中學(xué)高二階段練習(xí)）已知SKIPIF1<0、SKIPIF1<0，直線SKIPIF1<0過點(diǎn)SKIPIF1<0，且與線段SKIPIF1<0相交，則直線SKIPIF1<0的斜率取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·遼寧·大連市第二十三中學(xué)高二期中）已知直線SKIPIF1<0和以SKIPIF1<0，SKIPIF1<0為端點(diǎn)的線段相交，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<03．（2022·廣東·深圳中學(xué)高二期中）已知點(diǎn)SKIPIF1<0，SKIPIF1<0，若點(diǎn)SKIPIF1<0在線段AB上，則SKIPIF1<0的取值范圍（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·四川省瀘縣第四中學(xué)高二期中（文））已知直線SKIPIF1<0與曲線SKIPIF1<0有兩個(gè)不同的交點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是________.突破二：兩條直線平行與垂直1．（2022·江蘇南通·高二期中）SKIPIF1<0是直線SKIPIF1<0與直線SKIPIF1<0平行的（

）條件A．充分不必要 B．必要不充分C．充要 D．既非充分又非必要2．（2022·湖北宜昌·高二期中）若直線SKIPIF1<0：SKIPIF1<0與SKIPIF1<0：SKIPIF1<0平行，則實(shí)數(shù)SKIPIF1<0（

）A．2 B．－2 C．SKIPIF1<0 D．SKIPIF1<03．（2022·福建省福州第十一中學(xué)高三期中）已知SKIPIF1<0，SKIPIF1<0，直線SKIPIF1<0與直線SKIPIF1<0垂直，則SKIPIF1<0的最小值是___________.4．（2022·浙江·元濟(jì)高級中學(xué)高二期中）已知直線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0_________．突破三：直線方程1．（2022·北京四中高二期中）與直線SKIPIF1<0平行，且與圓SKIPIF1<0相切的直線方程為______.2．（2022·福建·晉江市季延中學(xué)高二期中）直線SKIPIF1<0被圓SKIPIF1<0截得的弦長為定值，則直線l的方程為_________________________．3．（2022·遼寧沈陽·高二期中）直線l過點(diǎn)SKIPIF1<0，若點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為3，則直線SKIPIF1<0的方程為______.4．（2022·廣東湛江·高三階段練習(xí)）寫出與直線SKIPIF1<0垂直且和圓SKIPIF1<0相切的一條直線的方程：__________．突破四：距離問題1．（2022·浙江·高二期中）點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．SKIPIF1<02．（2022·湖北宜昌·高二期中）函數(shù)SKIPIF1<0的最小值是（

）A．5 B．4 C．SKIPIF1<0 D．SKIPIF1<03．（2022·北京工業(yè)大學(xué)附屬中學(xué)高二期中）著名數(shù)學(xué)家華羅庚曾說過：“數(shù)無形時(shí)少直覺，形少數(shù)時(shí)難入微.”事實(shí)上，有很多代數(shù)問題可以轉(zhuǎn)化為幾何問題加以解決，如：SKIPIF1<0可以轉(zhuǎn)化為平面上點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0的距離.結(jié)合上述觀點(diǎn)，可得SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·福建省廈門第二中學(xué)高二階段練習(xí)）點(diǎn)SKIPIF1<0到直線SKIPIF1<0（SKIPIF1<0為任意實(shí)數(shù)）的距離的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·山東青島·高二期中）直線SKIPIF1<0過點(diǎn)SKIPIF1<0，SKIPIF1<0和SKIPIF1<0兩點(diǎn)到直線l的距離相等，則直線l的方程為（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<06．（2022·遼寧省康平縣高級中學(xué)高二期中）若圓M：SKIPIF1<0上至少有3個(gè)點(diǎn)到直線l：SKIPIF1<0的距離為SKIPIF1<0，則k的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．（2022·河北·石家莊市第十八中學(xué)高二階段練習(xí)）若第一象限內(nèi)的點(diǎn)SKIPIF1<0關(guān)于直線SKIPIF1<0的對稱點(diǎn)在直線SKIPIF1<0上，則SKIPIF1<0的最小值是（

）A．25 B．SKIPIF1<0 C．17 D．SKIPIF1<08．（2022·湖北·高二階段練習(xí)）平面直角坐標(biāo)系中有點(diǎn)SKIPIF1<0，SKIPIF1<0，直線SKIPIF1<0經(jīng)過點(diǎn)SKIPIF1<0，且SKIPIF1<0點(diǎn)到直線SKIPIF1<0的距離是SKIPIF1<0，則直線SKIPIF1<0的方程是__________．9．（2022·河南·宜陽縣第一高級中學(xué)高二階段練習(xí)）已知直線SKIPIF1<0與SKIPIF1<0平行，則SKIPIF1<0，SKIPIF1<0間的距離為___________.10．（2022·黑龍江省饒河縣高級中學(xué)高二階段練習(xí)）已知直線SKIPIF1<0，SKIPIF1<0，則直線SKIPIF1<0與SKIPIF1<0之間的距離最大值為______.11．（2022·江蘇·蘇州市相城區(qū)陸慕高級中學(xué)高二階段練習(xí)）實(shí)數(shù)SKIPIF1<0滿足：SKIPIF1<0，則SKIPIF1<0的最小值為________12．（2022·遼寧·東北育才學(xué)校高二階段練習(xí)）若實(shí)數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的最小值為______.13．（2022·上海市嘉定區(qū)第二中學(xué)高二期中）已知SKIPIF1<0為直線SKIPIF1<0上的動(dòng)點(diǎn)，SKIPIF1<0，則m的最小值為___________.突破五：圓的方程1．（2022·北京豐臺(tái)二中高三階段練習(xí)）若直線SKIPIF1<0截取圓SKIPIF1<0所得弦長為2，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．SKIPIF1<02．（2022·全國·高二課時(shí)練習(xí)）已知直線SKIPIF1<0恒過定點(diǎn)P，則與圓C：SKIPIF1<0有公共的圓心且過點(diǎn)P的圓的標(biāo)準(zhǔn)方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·安徽·合肥市第七中學(xué)高二期中）已知方程SKIPIF1<0表示圓，則k的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國·高二課時(shí)練習(xí)）已知SKIPIF1<0，則SKIPIF1<0的外接圓的方程是___________．5．（2022·江西·高三階段練習(xí)（文））設(shè)圓心SKIPIF1<0在直線SKIPIF1<0與直線SKIPIF1<0上，點(diǎn)SKIPIF1<0在SKIPIF1<0上，則SKIPIF1<0的方程為______．突破六：與圓上點(diǎn)有關(guān)的距離最值問題1．（2022·黑龍江·綏棱縣第一中學(xué)高三階段練習(xí)）已知圓C：SKIPIF1<0上的點(diǎn)到直線l：SKIPIF1<0的最大距離為M?最小距離為m，若SKIPIF1<0，則實(shí)數(shù)k的值是（

）A．SKIPIF1<0 B．1 C．SKIPIF1<0或1 D．SKIPIF1<0或12．（2022·貴州貴陽·高二階段練習(xí)）直線SKIPIF1<0被圓SKIPIF1<0截得的最短弦長為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·模擬預(yù)測）已知點(diǎn)P是曲線SKIPIF1<0上的動(dòng)點(diǎn)，則點(diǎn)P到直線SKIPIF1<0的距離的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·吉林吉林·高二期中）已知SKIPIF1<0是圓SKIPIF1<0上的一點(diǎn)，則SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·安徽省泗縣第一中學(xué)高二期中）直線SKIPIF1<0分別與SKIPIF1<0軸，SKIPIF1<0軸交于SKIPIF1<0兩點(diǎn)，點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，則SKIPIF1<0面積的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·河南·民權(quán)縣第一高級中學(xué)模擬預(yù)測（文））已知圓SKIPIF1<0的方程為SKIPIF1<0，SKIPIF1<0是圓SKIPIF1<0上一動(dòng)點(diǎn)，點(diǎn)SKIPIF1<0，SKIPIF1<0為線段SKIPIF1<0的中點(diǎn)，則SKIPIF1<0的最小值為__________.7．（2022·北京市第五十七中學(xué)高三階段練習(xí)）若點(diǎn)SKIPIF1<0在半徑為1，且圓心為坐標(biāo)原點(diǎn)的圓上，過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的切線，切點(diǎn)為SKIPIF1<0，則SKIPIF1<0的最小值為___________.8．（2022·湖南·衡陽市一中高二期中）已知SKIPIF1<0是曲線SKIPIF1<0上兩個(gè)不同的點(diǎn)，SKIPIF1<0，則SKIPIF1<0的最大值與最小值的比值是__________．9．（2022·上海市青浦高級中學(xué)高二階段練習(xí)）一束光線從點(diǎn)SKIPIF1<0射出，經(jīng)SKIPIF1<0軸上一點(diǎn)SKIPIF1<0反射后到達(dá)圓SKIPIF1<0上一點(diǎn)SKIPIF1<0，則SKIPIF1<0的最小值為_____．10．（2022·貴州·高三階段練習(xí)（文））已知O是坐標(biāo)原點(diǎn)，A，B是圓O：SKIPIF1<0上兩點(diǎn)，且SKIPIF1<0，若弦SKIPIF1<0的中點(diǎn)為SKIPIF1<0，則SKIPIF1<0的最小值為___________.突破七：圓的切線問題1．（2022·江蘇連云港·高二期末）從圓SKIPIF1<0外一點(diǎn)SKIPIF1<0向圓引切線，則此切線的長為（

）A．1 B．SKIPIF1<0 C．2 D．32．（2022·全國·高三專題練習(xí)）已知直線SKIPIF1<0是圓SKIPIF1<0：SKIPIF1<0的對稱軸，過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的一條切線，切點(diǎn)為SKIPIF1<0，則SKIPIF1<0等于（

）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·遼寧鞍山·高二期中）過點(diǎn)SKIPIF1<0引圓SKIPIF1<0的切線，則切線的方程為（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<04．（2022·四川省南充高級中學(xué)高二階段練習(xí)（理））若圓C:SKIPIF1<0上任意一點(diǎn)關(guān)于直線SKIPIF1<0的對稱點(diǎn)都在圓SKIPIF1<0上，由點(diǎn)SKIPIF1<0向圓SKIPIF1<0作切線，則切線段長的最小值為（

）A．2 B．3 C．4 D．65．（2022·全國·高二課時(shí)練習(xí)）過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的切線SKIPIF1<0，則切線SKIPIF1<0的方程為_________．6．（2022·全國·高二課時(shí)練習(xí)）曲線SKIPIF1<0與直線l：y＝k（x－2）＋4有兩個(gè)交點(diǎn)，則實(shí)數(shù)k的取值范圍是________．突破八：兩圓的公共弦問題1．（2022·四川·成都七中高二期中（文））圓SKIPIF1<0?與圓SKIPIF1<0?公共弦所在直線方程為___________．2．（2022·四川成都·高二期中（文））圓SKIPIF1<0與圓SKIPIF1<0的公共弦長為______．3．（2022·天津·耀華中學(xué)高二期中）兩圓SKIPIF1<0和SKIPIF1<0相交于兩點(diǎn)SKIPIF1<0，則公共弦SKIPIF1<0的長為__________.4．（2022·四川省綿陽南山中學(xué)高二階段練習(xí)（理））過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的兩條切線，切點(diǎn)分別為A，B，則直線AB的方程為_____．（請用直線方程的一般式作答）突破九：圓的弦長問題1．（2022·天津市第二耀華中學(xué)高三階段練習(xí)）若直線SKIPIF1<0被圓SKIPIF1<0截得線段的長為6，則實(shí)數(shù)SKIPIF1<0的值為__________.2．（2022·四川省綿陽江油中學(xué)模擬預(yù)測（理））若直線SKIPIF1<0過SKIPIF1<0，且被圓SKIPIF1<0截得的弦長為SKIPIF1<0，則直線SKIPIF1<0方程為______3．（2022·廣東·模擬預(yù)測）若斜率為SKIPIF1<0的直線與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0，與圓SKIPIF1<0相交于點(diǎn)SKIPIF1<0兩點(diǎn)，若SKIPIF1<0，則SKIPIF1<0______．4．（2022·河南·高二階段練習(xí)（文））過點(diǎn)SKIPIF1<0作一條直線與圓SKIPIF1<0分別交于M，N兩點(diǎn).若弦MN的長為SKIPIF1<0，則直線MN的方程為______.5．（2022·山西運(yùn)城·高二階段練習(xí)）已知圓SKIPIF1<0過平面內(nèi)三點(diǎn)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．(1)求圓SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)若點(diǎn)B也在圓SKIPIF1<0上，且弦AB長為SKIPIF1<0，求直線AB的方程．6．（2022·福建·廈門外國語學(xué)校石獅分校高二期中）已知圓SKIPIF1<0:SKIPIF1<0，點(diǎn)SKIPIF1<0坐標(biāo)為SKIPIF1<0，SKIPIF1<0為圓SKIPIF1<0上動(dòng)點(diǎn)，SKIPIF1<0中點(diǎn)為SKIPIF1<0.(1)當(dāng)點(diǎn)SKIPIF1<0在圓SKIPIF1<0上動(dòng)時(shí)，求點(diǎn)SKIPIF1<0的軌跡方程；(2)過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與SKIPIF1<0的軌跡相交于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，求直線SKIPIF1<0的方程.7．（2022·北京市師達(dá)中學(xué)高二階段練習(xí)）已知圓SKIPIF1<0，直線SKIPIF1<0.(1)若直線SKIPIF1<0與圓SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，SKIPIF1<0，求SKIPIF1<0的值.(2)求證：無論SKIPIF1<0取什么實(shí)數(shù)，直線SKIPIF1<0與圓SKIPIF1<0恒交于兩點(diǎn)；(3)求直線SKIPIF1<0被圓SKIPIF1<0截得的最短弦長，以及此時(shí)直線SKIPIF1<0的方程.8．（2022·遼寧·本溪滿族自治縣高級中學(xué)高二階段練習(xí)）已知直線SKIPIF1<0經(jīng)過直線SKIPIF1<0和SKIPIF1<0的交點(diǎn)，且與直線SKIPIF1<0垂直.(1)求直線SKIPIF1<0的方程；(2)若圓SKIPIF1<0過點(diǎn)SKIPIF1<0，且圓心SKIPIF1<0在SKIPIF1<0軸的負(fù)半軸上，直線SKIPIF1<0被圓SKIPIF1<0所截得的弦長為SKIPIF1<0，求圓SKIPIF1<0的標(biāo)準(zhǔn)方程.9．（2022·山東省濟(jì)南市萊鋼高級中學(xué)高二期中）已知圓SKIPIF1<0和點(diǎn)SKIPIF1<0．(1)過點(diǎn)M向圓O引切線，求切線的方程；(2)求以點(diǎn)M為圓心，且被直線SKIPIF1<0截得的弦長為8的圓M的方程；10．（2022·貴州貴陽·高二階段練習(xí)）已知圓SKIPIF1<0的圓心在直線SKIPIF1<0上，且與直線SKIPIF1<0相切于點(diǎn)SKIPIF1<0.(1)求圓SKIPIF1<0的方程；(2)若過點(diǎn)SKIPIF1<0的直線SKIPIF1<0被圓SKIPIF1<0截得的弦SKIPIF1<0的長為4，求直線SKIPIF1<0的方程.第三部分：沖刺重難點(diǎn)特訓(xùn)一、單選題1．（2022·浙江省杭州第九中學(xué)高二期中）直線SKIPIF1<0的傾斜角為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·浙江·杭州市源清中學(xué)高二期中）已知直線的方程為SKIPIF1<0，則該直線的傾斜角為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·浙江大學(xué)附屬中學(xué)高二期中）已知x，y滿足SKIPIF1<0，若不等式SKIPIF1<0恒成立，則c的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·浙江大學(xué)附屬中學(xué)高二期中）若直線SKIPIF1<0與SKIPIF1<0互相垂直，則實(shí)數(shù)SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或0 D．SKIPIF1<0或05．（2022·河北·任丘市第一中學(xué)高二階段練習(xí)）已知圓SKIPIF1<0與圓SKIPIF1<0的公共弦所在直線恒過點(diǎn)SKIPIF1<0，且點(diǎn)SKIPIF1<0在直線SKIPIF1<0上，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·河北·涉縣第一中學(xué)高三期中）過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的切線，則切線方程為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·河南·馬店第一高級中學(xué)模擬預(yù)測（理））已知?jiǎng)狱c(diǎn)M，N分別在拋物線SKIPIF1<0：SKIPIF1<0和圓SKIPIF1<0：SKIPIF1<0上，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．5 D．68．（2022·湖南長沙·高二階段練習(xí)）已知直線SKIPIF1<0：SKIPIF1<0和圓SKIPIF1<0：SKIPIF1<0交于A，B兩點(diǎn)，則弦AB所對的圓心角的余弦值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2022·四川·威遠(yuǎn)中學(xué)校高二期中（文））一條光線從點(diǎn)SKIPIF1<0射出，經(jīng)x軸反射后，與圓SKIPIF1<0相切，則反射后光線所在的直線方程為（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0SKIPIF1<010．（2022·四川省遂寧高級實(shí)驗(yàn)學(xué)校高二期中（理））已知圓SKIPIF1<0，圓SKIPIF1<0，過圓SKIPIF1<0上任意一點(diǎn)SKIPIF1<0作圓SKIPIF1<0的兩條切線SKIPIF1<0、SKIPIF1<0切點(diǎn)分別為SKIPIF1<0、SKIPIF1<0，則SKIPIF1<0的最小值是（

）A．SKIPIF1<0 B．3 C．SKIPIF1<0 D．SKIPIF1<011．（2022·江蘇·南京市天印高級中學(xué)高二階段練習(xí)）若圓SKIPIF1<0與圓SKIPIF1<0關(guān)于直線SKIPIF1<0對稱，圓SKIPIF1<0上任意一點(diǎn)SKIPIF1<0均滿足SKIPIF1<0，其中SKIPIF1<0，SKIPIF1<0為坐標(biāo)原點(diǎn)，則圓SKIPIF1<0和圓SKIPIF1<0的公切線有（

）A．1條 B．2條 C．3條 D．4條二、多選題12．（2022·浙江·杭州市源清中學(xué)高二期中）已知圓SKIPIF1<0，則下列說法正確的是（

）A．點(diǎn)SKIPIF1<0在圓內(nèi) B．圓M關(guān)于SKIPIF1<0對稱C．直線SKIPIF1<0與截圓M的弦長為SKIPIF1<0 D．直線SKIPIF1<0與圓M相切13．（2022·浙江大學(xué)附屬中學(xué)高二期中）設(shè)動(dòng)直線SKIPIF1<0交圓SKIPIF1<0于A，B兩點(diǎn)（C為圓心），則下列說法正確的有（

）A．直線l過定點(diǎn)SKIPIF1<0 B．當(dāng)SKIPIF1<0取得最大值時(shí)，SKIPIF1<0C．當(dāng)SKIPIF1<0最小時(shí)，其余弦值SKIPIF1<0 D．SKIPIF1<0的取值范圍是SKIPIF1<014．（2022·福建省南安國光中學(xué)高三階段練習(xí)）已知圓SKIPIF1<0（SKIPIF1<0為圓心），直線SKIPIF1<0，點(diǎn)SKIPIF1<0在直線SKIPIF1<0上運(yùn)動(dòng)，直線SKIPIF1<0分別與圓SKIPIF1<0切于點(diǎn)SKIPIF1<0．則下