新高考數(shù)學(xué)一輪復(fù)習(xí)講練測第8章第04講 直線與圓、圓與圓的位置關(guān)系（練習(xí)）（原卷版）

第04講直線與圓、圓與圓的位置關(guān)系（模擬精練+真題演練）1．（2023·廣東深圳·統(tǒng)考二模）若過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與圓SKIPIF1<0交于SKIPIF1<0兩點(diǎn)，則弦SKIPIF1<0最短時直線SKIPIF1<0的方程為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023·云南·云南師大附中?？寄M預(yù)測）已知圓SKIPIF1<0：SKIPIF1<0，直線SKIPIF1<0：SKIPIF1<0被圓SKIPIF1<0截得的弦長為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·河南·校聯(lián)考模擬預(yù)測）已知圓SKIPIF1<0的直徑SKIPIF1<0，若平面內(nèi)一個動點(diǎn)SKIPIF1<0與點(diǎn)SKIPIF1<0的距離是它與點(diǎn)SKIPIF1<0距離的SKIPIF1<0倍，則SKIPIF1<0的面積的最大值為（

）A．64 B．12 C．SKIPIF1<0 D．SKIPIF1<04．（2023·福建泉州·泉州五中校考模擬預(yù)測）若點(diǎn)SKIPIF1<0是圓SKIPIF1<0：SKIPIF1<0上的任一點(diǎn)，直線SKIPIF1<0：SKIPIF1<0與SKIPIF1<0軸、SKIPIF1<0軸分別交于SKIPIF1<0兩點(diǎn)，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．85．（2023·重慶·統(tǒng)考模擬預(yù)測）已知過拋物線SKIPIF1<0焦點(diǎn)的直線與拋物線C交于A，B兩點(diǎn)，且SKIPIF1<0，圓SKIPIF1<0，若拋物線C與圓SKIPIF1<0交于P，Q兩點(diǎn)，且SKIPIF1<0，則線段SKIPIF1<0的中點(diǎn)D的橫坐標(biāo)為（

）A．2 B．3 C．4 D．56．（2023·黑龍江哈爾濱·哈師大附中?？寄M預(yù)測）圓SKIPIF1<0：SKIPIF1<0與直線SKIPIF1<0：SKIPIF1<0交于SKIPIF1<0、SKIPIF1<0，當(dāng)SKIPIF1<0最小時，SKIPIF1<0的值為（

）A．SKIPIF1<0 B．2 C．SKIPIF1<0 D．17．（2023·北京·北京八十中?？寄M預(yù)測）已知直線SKIPIF1<0與圓SKIPIF1<0交于A，B兩點(diǎn)，O是原點(diǎn)，C是圓上一點(diǎn)，若SKIPIF1<0，則a的值為（

）．A．1 B．SKIPIF1<0 C．2 D．48．（2023·云南昭通·校聯(lián)考模擬預(yù)測）已知SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0為圓SKIPIF1<0上任意一點(diǎn)，則SKIPIF1<0面積的最大值為（

）A．5 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2023·福建三明·統(tǒng)考三模）角SKIPIF1<0的頂點(diǎn)在坐標(biāo)原點(diǎn)，始邊與SKIPIF1<0軸的非負(fù)半軸重合，終邊不在坐標(biāo)軸上，終邊所在的直線與圓SKIPIF1<0相交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)，當(dāng)SKIPIF1<0面積最大時SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2023·河南·河南省內(nèi)鄉(xiāng)縣高級中學(xué)?？寄M預(yù)測）已知函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值與最小值分別為SKIPIF1<0和SKIPIF1<0，則經(jīng)過函數(shù)SKIPIF1<0的圖象的對稱中心的直線被圓SKIPIF1<0截得的最短弦長為（

）A．10 B．5 C．SKIPIF1<0 D．SKIPIF1<011．（多選題）（2023·海南?？凇ずＤ先A僑中學(xué)?？家荒＃┤鐖D所示，該曲線W是由4個圓：SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的一部分所構(gòu)成，則下列敘述正確的是（

）

A．曲線W圍成的封閉圖形面積為4+2πB．若圓SKIPIF1<0與曲線W有8個交點(diǎn)，則SKIPIF1<0C．SKIPIF1<0與SKIPIF1<0的公切線方程為SKIPIF1<0D．曲線W上的點(diǎn)到直線SKIPIF1<0的距離的最小值為412．（多選題）（2023·湖南·校聯(lián)考二模）已知點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，則（

）A．兩圓外離 B．SKIPIF1<0的最大值為9C．SKIPIF1<0的最小值為1 D．兩個圓的一條公切線方程為SKIPIF1<013．（多選題）（2023·湖南·校聯(lián)考模擬預(yù)測）已知圓SKIPIF1<0，直線SKIPIF1<0，則（

）A．直線SKIPIF1<0恒過定點(diǎn)B．直線SKIPIF1<0能表示平面直角坐標(biāo)系內(nèi)每一條直線C．對任意實(shí)數(shù)SKIPIF1<0，直線SKIPIF1<0都與圓SKIPIF1<0相交D．直線SKIPIF1<0被圓SKIPIF1<0截得的弦長的最小值為SKIPIF1<014．（多選題）（2023·江蘇·統(tǒng)考模擬預(yù)測）古希臘著名數(shù)學(xué)家阿波羅尼斯發(fā)現(xiàn)：平面內(nèi)到兩個定點(diǎn)SKIPIF1<0，SKIPIF1<0的距離之比為定值SKIPIF1<0的點(diǎn)的軌跡是圓，此圓被稱為“阿波羅尼斯圓”．在平面直角坐標(biāo)系SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0滿足SKIPIF1<0．設(shè)點(diǎn)SKIPIF1<0的軌跡為SKIPIF1<0，則（

）．A．軌跡SKIPIF1<0的方程為SKIPIF1<0B．在SKIPIF1<0軸上存在異于SKIPIF1<0，SKIPIF1<0的兩點(diǎn)SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0C．當(dāng)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0三點(diǎn)不共線時，射線SKIPIF1<0是SKIPIF1<0的角平分線D．在SKIPIF1<0上存在點(diǎn)SKIPIF1<0，使得SKIPIF1<015．（多選題）（2023·全國·模擬預(yù)測）過圓SKIPIF1<0上一點(diǎn)P作圓SKIPIF1<0的兩條切線，切點(diǎn)分別為A，B，則（

）.A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．直線AB與圓SKIPIF1<0相切16．（多選題）（2023·江蘇徐州·?？寄M預(yù)測）已知圓SKIPIF1<0的方程為SKIPIF1<0，點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0是SKIPIF1<0軸上的一個動點(diǎn)，過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的兩條切線，切點(diǎn)分別為SKIPIF1<0，則（

）A．存在切點(diǎn)SKIPIF1<0使得SKIPIF1<0為直角 B．直線SKIPIF1<0過定點(diǎn)SKIPIF1<0C．SKIPIF1<0的取值范圍是SKIPIF1<0 D．SKIPIF1<0面積的取值范圍是SKIPIF1<017．（2023·四川成都·校聯(lián)考模擬預(yù)測）已知圓SKIPIF1<0與圓SKIPIF1<0：SKIPIF1<0相內(nèi)切，則實(shí)數(shù)m的值為．18．（2023·北京·北京四中?？寄M預(yù)測）已知圓SKIPIF1<0，若點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，并且點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為SKIPIF1<0，則滿足條件的點(diǎn)SKIPIF1<0的個數(shù)為.19．（2023·河南開封·統(tǒng)考三模）已知點(diǎn)M在圓SKIPIF1<0上，直線SKIPIF1<0與x軸、y軸的交點(diǎn)分別A、B，則SKIPIF1<0的最小值為.20．（2023·四川綿陽·綿陽南山中學(xué)實(shí)驗(yàn)學(xué)校校考三模）已知SKIPIF1<0的圓心在曲線SKIPIF1<0上，且SKIPIF1<0與直線SKIPIF1<0相切，則SKIPIF1<0的面積的最小值為.21．（2023·江蘇揚(yáng)州·統(tǒng)考模擬預(yù)測）圓SKIPIF1<0（SKIPIF1<0為坐標(biāo)原點(diǎn)）與直線SKIPIF1<0相切，與直線SKIPIF1<0垂直的直線SKIPIF1<0與圓SKIPIF1<0交于不同的兩點(diǎn)SKIPIF1<0，若SKIPIF1<0，則直線SKIPIF1<0的縱截距的取值范圍是．22．（2023·湖北武漢·華中師大一附中?？寄M預(yù)測）SKIPIF1<0中，SKIPIF1<0是邊SKIPIF1<0上的點(diǎn)，SKIPIF1<0，且SKIPIF1<0．(1)若SKIPIF1<0，求SKIPIF1<0面積的最大值；(2)若SKIPIF1<0內(nèi)是否存在點(diǎn)SKIPIF1<0，使得SKIPIF1<0？若存在，求SKIPIF1<0；若不存在，說明理由．1．（2022?上海）設(shè)集合SKIPIF1<0，SKIPIF1<0，SKIPIF1<0①存在直線SKIPIF1<0，使得集合SKIPIF1<0中不存在點(diǎn)在SKIPIF1<0上，而存在點(diǎn)在SKIPIF1<0兩側(cè)；②存在直線SKIPIF1<0，使得集合SKIPIF1<0中存在無數(shù)點(diǎn)在SKIPIF1<0上；SKIPIF1<0SKIPIF1<0A．①成立②成立 B．①成立②不成立 C．①不成立②成立 D．①不成立②不成立2．（2021?北京）已知直線SKIPIF1<0為常數(shù)）與圓SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0變化時，若SKIPIF1<0的最小值為2，則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2021?全國）已知點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，則SKIPIF1<0到直線SKIPIF1<0距離的最小值為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2020?新課標(biāo)Ⅲ）若直線SKIPIF1<0與曲線SKIPIF1<0和圓SKIPIF1<0都相切，則SKIPIF1<0的方程為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2020?新課標(biāo)Ⅰ）已知圓SKIPIF1<0，過點(diǎn)SKIPIF1<0的直線被該圓所截得的弦的長度的最小值為SKIPIF1<0SKIPIF1<0A．1 B．2 C．3 D．46．（2020?新課標(biāo)Ⅰ）已知SKIPIF1<0，直線SKIPIF1<0，SKIPIF1<0為SKIPIF1<0上的動點(diǎn)．過點(diǎn)SKIPIF1<0作SKIPIF1<0的切線SKIPIF1<0，SKIPIF1<0，切點(diǎn)為SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0最小時，直線SKIPIF1<0的方程為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（多選題）（2021?新高考Ⅰ）已知點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，點(diǎn)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0SKIPIF1<0A．點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離小于10 B．點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離大于2 C．當(dāng)SKIPIF1<0最小時，SKIPIF1<0 D．當(dāng)SKIPIF1<0最大時，SKIPIF1<08．（多選題）（2021?新高考Ⅱ）已知直線SKIPIF1<0與圓SKIPIF1<0，點(diǎn)SKIPIF1<0，則下列說法正確的是SKIPIF1<0SKIPIF1<0A．若點(diǎn)SKIPIF1<0在圓SKIPIF1<0上，則直線SKIPIF1<0與圓SKIPIF1<0相切 B．若點(diǎn)SKIPIF1<0在圓SKIPIF1<0外，則直線SKIPIF1<0與圓SKIPIF1<0相離 C．若點(diǎn)SKIPIF1<0在直線SKIPIF1<0上，則直線SKIPIF1<0與圓SKIPIF1<0相切 D．若點(diǎn)SKIPIF1<0在圓SKIPIF1<0內(nèi)，則直線SKIPIF1<0與圓SKIPIF1<0相離9．（2023?天津）過原點(diǎn)的一條直線與圓SKIPIF1<0相切，交曲線SKIPIF1<0于點(diǎn)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的值為．10．（2023?新高考Ⅱ）已知直線SKIPIF1<0與SKIPIF1<0交于SKIPIF1<0，SKIPI