新高考數(shù)學(xué)一輪復(fù)習(xí)精講精練10.2 圓的方程（基礎(chǔ)版）（原卷版）

10.2圓的方程（精講）（基礎(chǔ)版）思維導(dǎo)圖思維導(dǎo)圖考點(diǎn)呈現(xiàn)考點(diǎn)呈現(xiàn)例題剖析例題剖析考點(diǎn)一圓的方程【例1-1】（2021白云期末）已知圓SKIPIF1<0的方程為SKIPIF1<0，則圓心SKIPIF1<0的坐標(biāo)為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例1-2】（2022成都）已知圓SKIPIF1<0的圓心在直線SKIPIF1<0上，且圓SKIPIF1<0與SKIPIF1<0軸的交點(diǎn)分別為SKIPIF1<0，則圓SKIPIF1<0的標(biāo)準(zhǔn)方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·江西模擬）設(shè)甲：實(shí)數(shù)SKIPIF1<0；乙：方程SKIPIF1<0是圓，則甲是乙的（）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分也不必要條件2．（2022和平）圓心在SKIPIF1<0軸上，半徑為2，且過點(diǎn)SKIPIF1<0的圓的方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022杭州）過點(diǎn)（7，-2）且與直線SKIPIF1<0相切的半徑最小的圓方程是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)二直線與圓的位置關(guān)系【例2-1】（2022高二下·玉溪期末）已知直線SKIPIF1<0經(jīng)過點(diǎn)SKIPIF1<0，且SKIPIF1<0與圓SKIPIF1<0相切，則SKIPIF1<0的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2022·溫州）已知直線SKIPIF1<0與圓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（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-3】（2022·柳州模擬）已知直線SKIPIF1<0與圓SKIPIF1<0相交于A，B兩點(diǎn)SKIPIF1<0，則k＝（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·秦皇島二模）直線SKIPIF1<0被圓SKIPIF1<0截得的弦長為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·呼和浩特模擬）直線l：SKIPIF1<0與函數(shù)SKIPIF1<0的圖象有兩個(gè)公共點(diǎn)，則k的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·貴陽模擬）已知直線SKIPIF1<0和SKIPIF1<0與圓SKIPIF1<0都相切，則圓SKIPIF1<0的面積的最大值是（）A．2π B．4π C．8π D．16π4．（2022·鞍山模擬）（多選）已知M為圓C：SKIPIF1<0上的動(dòng)點(diǎn)，P為直線l：SKIPIF1<0上的動(dòng)點(diǎn)，則下列結(jié)論正確的是（）A．直線l與圓C相切 B．直線l與圓C相離C．|PM|的最大值為SKIPIF1<0 D．|PM|的最小值為SKIPIF1<0考點(diǎn)三圓與圓的位置關(guān)系【例3-1】（2022高一下·漢中期中）已知SKIPIF1<0，SKIPIF1<0，那么它們的位置關(guān)系是（）A．外離 B．相切 C．相交 D．內(nèi)含【例3-2】（2022·吉林模擬）已知兩圓方程分別為SKIPIF1<0和SKIPIF1<0．則兩圓的公切線有（）A．1條 B．2條 C．3條 D．4條【一隅三反】1．（2022·石家莊模擬）（多選）已知圓SKIPIF1<0與圓SKIPIF1<0，則下列說法正確的是（）A．若圓SKIPIF1<0與x軸相切，則SKIPIF1<0B．若SKIPIF1<0，則圓SKIPIF1<0與圓SKIPIF1<0相離C．若圓SKIPIF1<0與圓SKIPIF1<0有公共弦，則公共弦所在的直線方程為SKIPIF1<0D．直線SKIPIF1<0與圓SKIPIF1<0始終有兩個(gè)交點(diǎn)2．（2022·徐匯期末）已知圓SKIPIF1<0和圓SKIPIF1<0內(nèi)切，則m的值為．3（2022廣安期末）若圓SKIPIF1<0平分圓SKIPIF1<0的周長，則直線SKIPIF1<0被圓SKIPIF1<0所截得的弦長為．考點(diǎn)四切線問題【例4-1】（2022·天津市模擬）過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的切線SKIPIF1<0，則SKIPIF1<0的方程為（）A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<0【例4-2】（2022·湖北模擬）若圓SKIPIF1<0關(guān)于直線SKIPIF1<0對稱，則從點(diǎn)SKIPIF1<0向圓SKIPIF1<0作切線，切線長最小值為（）A．2 B．3 C．4 D．6【一隅三反】1．（2022·朝陽模擬）過點(diǎn)SKIPIF1<0作圓SKIPIF1<0的切線，則切線方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2022·廣西模擬）過圓SKIPIF1<0上一點(diǎn)A作圓SKIPIF1<0的切線，切點(diǎn)為B，則SKIPIF1<0的最小值為（）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022高二下·番禺期末）寫出與圓SKIPIF1<0和圓SKIPIF1<0都相切的一條切線方程.10.2圓的方程（精練）（基礎(chǔ)版）題組一題組一圓的方程1．（2022湖南期末）若SKIPIF1<0的三個(gè)頂點(diǎn)坐標(biāo)分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0外接圓的圓心坐標(biāo)為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022成都期末）已知圓SKIPIF1<0的圓心為SKIPIF1<0，且圓SKIPIF1<0與SKIPIF1<0軸的交點(diǎn)分別為SKIPIF1<0，則圓SKIPIF1<0的標(biāo)準(zhǔn)方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022天津月考）與SKIPIF1<0軸相切，且圓心坐標(biāo)為SKIPIF1<0的圓的標(biāo)準(zhǔn)方程為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國·高二課時(shí)練習(xí)）求滿足下列條件的圓的方程，并畫出圖形：(1)經(jīng)過點(diǎn)SKIPIF1<0和SKIPIF1<0，圓心在x軸上；(2)經(jīng)過直線SKIPIF1<0與SKIPIF1<0的交點(diǎn)，圓心為點(diǎn)SKIPIF1<0；(3)經(jīng)過SKIPIF1<0，SKIPIF1<0兩點(diǎn)，且圓心在直線SKIPIF1<0上；(4)經(jīng)過SKIPIF1<0，SKIPIF1<0，SKIPIF1<0三點(diǎn)．題組二直線與圓的位置關(guān)系題組二直線與圓的位置關(guān)系1（2022·濱州二模）已知直線SKIPIF1<0，圓SKIPIF1<0，則直線l與圓C的位置關(guān)系是（）A．相離 B．相切 C．相交 D．不確定2．（2022·畢節(jié)模擬）曲線SKIPIF1<0與直線SKIPIF1<0有兩個(gè)交點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022汕尾期末）（多選）直線SKIPIF1<0：SKIPIF1<0與圓SKIPIF1<0：SKIPIF1<0相交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，則（）A．直線SKIPIF1<0過定點(diǎn)SKIPIF1<0B．SKIPIF1<0時(shí)，直線SKIPIF1<0平分圓SKIPIF1<0C．SKIPIF1<0時(shí)，SKIPIF1<0為等腰直角三角形D．SKIPIF1<0時(shí)，弦SKIPIF1<0最短4．（2022廣東月考）（多選）已知點(diǎn)SKIPIF1<0是圓SKIPIF1<0上的任意一點(diǎn)，直線SKIPIF1<0，則下列結(jié)論正確的是（）A．直線SKIPIF1<0與圓SKIPIF1<0的位置關(guān)系只有相交和相切兩種B．圓SKIPIF1<0的圓心到直線SKIPIF1<0距離的最大值為SKIPIF1<0C．點(diǎn)SKIPIF1<0到直線SKIPIF1<0距離的最小值為SKIPIF1<0D．點(diǎn)SKIPIF1<0可能在圓SKIPIF1<0上5．（2022鹽城期末）已知直線SKIPIF1<0與圓SKIPIF1<0相切，則實(shí)數(shù)a的值為．6（2022·新高考Ⅱ卷）已知點(diǎn)SKIPIF1<0，若直線SKIPIF1<0關(guān)于SKIPIF1<0的對稱直線與圓SKIPIF1<0存在公共點(diǎn)，則實(shí)數(shù)a的取值范圍為．7．（2022廣東）當(dāng)圓SKIPIF1<0截直線SKIPIF1<0所得的弦長最短時(shí)，m的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．-1 D．18（2022山西）．過點(diǎn)SKIPIF1<0的直線l與圓SKIPIF1<0有公共點(diǎn)，則直線l傾斜角的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09（2022山東）．過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與圓SKIPIF1<0：SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，當(dāng)弦SKIPIF1<0取最大值時(shí)，直線SKIPIF1<0的方程為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0題組三題組三圓與圓的位置關(guān)系1．（2022·邯鄲模擬）已知圓SKIPIF1<0：SKIPIF1<0和圓SKIPIF1<0：SKIPIF1<0，則“SKIPIF1<0”是“圓SKIPIF1<0與圓SKIPIF1<0內(nèi)切”的（）A．充分不必要條件 B．必要不充分條件C．充分必要條件 D．既不充分也不必要條件2．（2022·河?xùn)|模擬）圓SKIPIF1<0與圓SKIPIF1<0的公共弦長為．3．（2022·河西模擬）設(shè)SKIPIF1<0與SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，則SKIPIF1<0．4．（2022·威海模擬）圓SKIPIF1<0與圓SKIPIF1<0的公共弦長為．5．（2022·湖南模擬）已知?jiǎng)訄ASKIPIF1<0與圓SKIPIF1<0外切，與圓SKIPIF1<0內(nèi)切，則動(dòng)圓圓心SKIPIF1<0的軌跡方程為．6．（2021·山東濟(jì)南市·高二期末）（多選）已知圓SKIPIF1<0和圓SKIPIF1<0的公共點(diǎn)為SKIPIF1<0，SKIPIF1<0，則（）A．SKIPIF1<0 B．直線SKIPIF1<0的方程是SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．（2021·全國高二課時(shí)練習(xí)）（多選）圓SKIPIF1<0和圓SKIPIF1<0的交點(diǎn)為A，B，則有（）A．公共弦AB所在直線方程為SKIPIF1<0B．線段AB中垂線方程為SKIPIF1<0C．公共弦AB的長為SKIPIF1<0D．P為圓SKIPIF1<0上一動(dòng)點(diǎn)，則P到直線AB距離的最大值為SKIPIF1<08．（2022云南）已知圓SKIPIF1<0與圓SKIPIF1<0．(1)求證：圓SKIPIF1<0與圓SKIPIF1<0相交；(2)求兩圓公共弦所在直線的方程；(3)求經(jīng)過兩圓交點(diǎn)，且圓心在直線SKIPIF1<0上的圓的方程．題組四題組四切線問題1．（2022哈爾濱）設(shè)圓SKIPIF1<0，圓SKIPIF1<0，則圓SKIPIF1<0，SKIPIF1<0