专题8.4直线与圆、圆与圆的位置关系十大题型（原卷版）_11.4-2_2026-11-04

      
      
专题8.4 直线与圆、圆与圆的位置关系【十大题型】

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C2 7
D 14
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3
B1
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D﹣2
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A1
B 3
C2
D2 3
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B2
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D4
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D𝑥= 1p24𝑥+ 7𝑦−48 = 0
Ġt 3-2Y2024·ĭĮĢł·ĞģĤĥZī‹!𝑂:𝑥2 + 𝑦2 = 1I›3𝑥+ 4𝑦−10 = 0-"ď.𝑃É!𝑂"
MÒ+I+.¬𝐴I£|𝑃𝐴|"6©7¬Y    Z
A1
B 2
C 3
D2
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C26
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1
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Bʼn1 p−2
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D1 pʼn1
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2𝑥−𝑦−1 = 0"01¬ 2I£Q
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 5  34*
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2
B
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34"6y7 6©7ŋŌlòY    Z
A12
B6 2
C6
D3 2
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𝑃𝑄¬¨"! !𝑄†“ò𝐴,𝐵9.I£Óŏs𝑃𝐴𝑄𝐵34"6©7¬Y   Z
A2 7
B4 7
C2
D4
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A 2
B2 2
C4 2
D8 2
 6   !#$%5"67*
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A 2
B2
C 6
D2 2
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A−2 5
5
B−
4
5
C−5
5
D−
3
5
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𝑘𝑥−𝑦−3𝑘+ 4 = 0 "01I £ª 𝜃，𝑘ĠiI 𝑑"6y7 6©7ŋŌ¬Y    Z
A2
B3
C4
D6
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𝑥2 + 𝑦2 = 1I.𝐴(2,0)I𝐵(0,2)I𝑃\Ş𝐴𝐵-"
ď.I›𝑃É!𝑂"+I+.A¶¬𝐶I𝐷I{n’Ó­ş
①Óŏs𝑃𝐶𝑂𝐷"34"6©7¬ 1z②
      
      
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3
2Î5®{Šîş
"š	¬Y   Z
A①③④
B①②④
C②③④
D①④
 7   !5"8.87*
ę 7Y2024 °·TU·ŢţZī‹!𝐴
(𝑥+ 2)2 + 𝑦2 = 25I𝐴¬!¦Iď𝑙›.𝑃(2,0)IÚ 
!𝐴“ò𝐵I𝐶9.Iŝ(𝐵𝐶"5.𝑄"Ťť¬…𝐸.
(1)<…𝐸"GHz
(2)›𝐴É9ÒôõA¶¬𝑘1I𝑘2"I“…𝐸ò𝑀I𝑁9.IÚ𝑘1𝑘2 = −3I<Ŧ
𝑀𝑁›8.
Ġt 7-1Y23-24 Ã-·ŐěŐĴ·œŔZī‹!¦𝐶€𝑦= −2𝑥-IŧÚĒ›.𝐴(2,−1)I 
𝑥+ 𝑦−1 = 0†+"!.
(1)<!𝐶"µŨGHz
(2)Ýò!𝐶-"ŊóM.𝑃I\ũö€8.𝐵Yx–òŁ.𝑂ZĺÂ
|𝑃𝐵|
|𝑃𝑂|Ū¬Æ
ū¡ö€I<~.𝐵"´µz
¡xö€IŬşŭ¥.
Ġt 7-2Y23-24 °-·ŮůŰűŲų·œŔZ!𝐺Ē›.(2,2 3),(−4,0)I!¦€𝑦= 𝑥-
(1)<!𝐺"µŨGHz
(2)¡!𝐺 𝑥‚A¶“ò𝑀,𝑁9.I𝐴¬𝑙:𝑥= 16-"ď.I𝐴𝑀,𝐴𝑁 …!𝐺"ŴM2“.A¶¬
𝐸,𝐹I<Ŧ𝐸𝐹Ē›8.Iŧ<~8."´µ
      
      
Ġt 7-3Y23-24 Ã-·ŵŰŶĴ·œ5Zī‹!𝐶›.𝐴(2,6)I!¦€𝑦= 𝑥+ 1-IĐ𝑦‚()¬2
5
(1)<!𝐶"GHz
(2)¡!𝐶§¨©ò10I.𝐷€Ĭ!-ĊďI.𝐵(3,2)Iŝ𝑀¬›𝐵,𝐷9."("5.I<𝑀"ŤťGHz
(3)€Y2Z"Òñ’I¡𝐵𝐷 𝑙:𝑦= 𝑥−2“ò.𝑁IŦŭ
|𝐵𝑀| ⋅|𝐵𝑁|Ū¬87
 8  ! !"#$%
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!"#$%¬Y   Z
A^Í
B†+
C†“
DÌ1
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%\Y    Z
A†“
BÌ+
C^+
D†1
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1
4
 !𝑂Y    Z
AÌ+
B†“
C^+
Dż{:.
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13I£!𝑀 !𝑁:(𝑥−2)2 + (𝑦+ 2)2 = 1"#$%\Y   Z
A†1
B†“
C^+
D^Í
 9  9!":(*
ę 9Y2024·ŮůŰ·ĞģĤĥZ!𝐶1:𝑥2 + 𝑦2−2𝑥= 10 !𝐶2:(𝑥+ 2)2 + (𝑦−4)2 = 16":()¬
Y    Z
A2 7
B 7
C 6
D2 6
Ġt 9-1Y2024·ŰĢŽŹ·ĞģĤĥZ!𝐶1:𝑥2 + 𝑦2 +2𝑥−8𝑦−8 = 0 !𝐶2:𝑥2 + 𝑦2 +4𝑥−4𝑦−4 = 0"
:()¬Y    Z
      
      
A 55
5
B2 55
5
C3 55
5
D4 55
5
Ġt 9-2Y2024·İĭžſƀ·ÃĞZī‹!𝑂1:𝑥2 + 𝑦2 = 5 !𝑂2:𝑥2 + 𝑦2−2𝑥−4𝑦= 0“ò AIB 9.I
£|𝐴𝐵| = Y     Z
A 5
2
B 5
C 15
D 15
2
Ġt 9-3Y2024·İı·ÃĞZ¡!𝐶1:𝑥2 + 𝑦2 = 1 !𝐶2:(𝑥−𝑎)2 + (𝑦−𝑏)2 = 1":( AB ")¬ 1I£
 AB "GH¬Y    Z
A2𝑎𝑥+ 𝑏𝑦−1 = 0
B2𝑎𝑥+ 𝑏𝑦−3 = 0
C2𝑎𝑥+ 2𝑏𝑦−1 = 0
D2𝑎𝑥+ 2𝑏𝑦−3 = 0
 10  9!"+*
ę 10Y2024·İĭžſƀ·°ĞZī‹!𝐶1:𝑥2 + 𝑦2 = 1J!𝐶2:𝑥2 + 𝑦2−6𝑥−8𝑦+ 9 = 0I£9!+"
Ò
¬Y    Z
A1
B2
C3
D4
Ġt 10-1Y23-24 °’·Ěě·ƁƂZ!𝐶1:𝑥2 + 𝑦2 +8𝑥−2𝑦+ 9 = 0J!𝐶2:𝑥2 + 𝑦2 +6𝑥−4𝑦+ 11 = 0
"+GH\Y    Z
A𝑦= −𝑥+ 1
B𝑦= −𝑥+ 1p𝑦= 𝑥+ 5
C𝑦= −𝑥+ 5
D𝑦= 𝑥+ 1p𝑦= 2𝑥+ 5
Ġt 10-2Y23-24 °-·Ěěƃƀ·œŔZī‹!𝐶1:(𝑥+ 1)2 + (𝑦+ 1)2 = 1I!𝐶2:𝑥2 + 𝑦2
−4𝑥−4𝑦−1 = 0I£9!"+Ò
¬Y    Z
A1
B2
C3
D4
Ġt 10-3Y23-24 °-·Ńń·ƄŞŢţZī‹!𝐶1:𝑥2 + 𝑦2 +4𝑥+ 3 = 0I!𝐶2:𝑥2 + 𝑦2−8𝑥+ 12 = 0I
’Ā5xC !𝐶1I𝐶2–i†+"\Y    Z
A 3𝑥+ 3𝑦= 0
B 3𝑥−3𝑦= 0
C𝑥+
35𝑦+ 8 = 0
D𝑥−35𝑦−8 = 0
M,P
1Y2024·ĭĮƅƆ·°ĞZī‹𝑙:𝑘𝑥−𝑦+ 1−𝑘= 0J! ⊙𝑂:𝑥2 + 𝑦2 = 𝑟2(𝑟> 0)I£“𝑟=
2”\“ö€Ƈ
M k ĺ l ⊙𝑂†+”"Y    Z
AĦAíxħ;Òñ
Bħ;íxĦAÒñ
      
      
CĦAħ;Òñ
DĨxĦA|xħ;Òñ
2Y2024·ƈƉƈĴ·ĞģĤĥZī‹!𝑥2 + 𝑦2 +4𝑚𝑥−2𝑚𝑦+ 𝑚= 0(𝑚∈𝑅) 𝑥‚†+I£𝑚= Y    Z
A1
B0 p
1
4
C0 p 1
D
1
4
3Y2024·ŮůŰűŲų·ĞģĤĥZī‹!𝐶1:𝑥2 + 𝑦2 = 4I!𝐶2:𝑥2 + 𝑦2−4𝑥−4𝑦+ 4 = 0I9!":(
®€GH\Y  Z
A𝑥+ 𝑦+ 2 = 0
B𝑥+ 𝑦−2 = 0
C𝑥+ 𝑦+ 1 = 0
D𝑥+ 𝑦−1 = 0
4Y2024·ƊƅĢĿ·ÃĞZī‹!𝐶:(𝑥−3)2 + (𝑦−4)2 = 9I𝑙:(𝑚+ 3)𝑥−(𝑚+ 2)𝑦+ 𝑚= 0.£𝑙IJ!
𝐶ĐÂ"()"6©7¬Y    Z
A2 7
B 10
C2 2
D 6
5Y2024·^ƋƌƍƎ·°ĞZī‹! 𝐶₁:(𝑥+ 1)2 + (𝑦+ 1)2 = 2，!𝐶2:𝑥2 + 𝑦2−4𝑥−4𝑦= 0，£9!"+
Ò
¬Y    Z
A4
B3
C2
D1
6Y2024·TU·ĞģĤĥZī‹ P ¬𝑙:𝑥−𝑦+ 1 = 0-M.I›. P É!𝐶:(𝑥−1)2 + 𝑦2 = 1"MÒ+I
+.¬ AI£|𝑃𝐴|"6©7¬Y    Z
A1
B 2
C 3
D2
7Y2024·ŐĢƏĴ·MĞZī‹. P ¬𝑙1:𝑚𝑥−2𝑦−𝑚+ 6 = 0 𝑙2:2𝑥+ 𝑚𝑦−𝑚−6 = 0(𝑚∈𝑅)"“
.I. Q ¬!𝐶:(𝑥+ 3)2 + (𝑦+ 3)2 = 8-"ď.I£|𝑃𝑄|"ü7ýþ¬Y    Z
A[2 2,8 2]
B(2 2,8 2]
C[ 2,6 2]
D( 2,6 2]
8Y2024·ŐĢıĿ·°ĞZī‹!𝐶:(𝑥−4)2 + 𝑦2 = 4I.𝑀€Ş𝑦= 𝑥Y0 ≤𝑥≤3Z-I›.𝑀É!𝐶"9
Ò+I+.A¶¬𝐴I𝐵In𝐴𝐵¬¨É!𝐶′I£!𝐶′"34"6y7¬Y    Z.
Aπ
B2π
C
5π
2
D3π
Ã,m
9Y2024·ŐĢ·ĞģĤĥZī‹𝑙:𝑦= 𝑘(𝑥−3) +3 …𝐶:𝑥2 + 𝑦2−2|𝑥|−2𝑦= 0{:.I£Ɛ
 k "
ü7Ån¬Y    Z
A0
B1
C2
D3
10Y2024·ĚěƑĩ·ĞģĤĥZī‹𝑙:𝑘𝑥−𝑦−2𝑘+ 3 = 0I!𝐶:𝑥2−2𝑥+ 𝑦2−8𝑦+ 13 = 0I£’Āş
Šî"\Y    Z
A!¦𝐶"´µ¬(1,4)
      
      
B𝑙 !𝐶ƒƓ{92“.
Cª𝑘= 2iI𝑙 !𝐶†“ò𝑀,𝑁9.I£ △𝐶𝑀𝑁"34¬3 11
10
D.𝐶/𝑙"016yiI𝑘= 1
11Y2024·ĚěƊƔ·°ĞZī‹ď.𝑀，𝑁 A¶€!𝐶1:(𝑥−1)2 + (𝑦−2)2 = 1 J 𝐶2:(𝑥−3)2 + (𝑦−4)2 = 3 
-Iď.𝑃 € 𝑥 ‚-I£Y     Z
A!𝐶2"§¨¬ 3
B!𝐶1J!𝐶2†1
C|𝑃𝑀| + |𝑃𝑁|"6©7¬2 10
D›.𝑃ƕ!𝐶1"+I£+)6ē¬ 3
°,qr
12Y2024·ġĢ·ĞģĤĥZ!(𝑥−𝑎)2 + (𝑦−2𝑎−3)2 = 9-Ėö€92./(2,3)"01¬ 1I£ a "ü7ý
þ\      .
13Y2024·ľĿƖƗ·ĞģĤĥZī‹!𝐶:𝑥2 + 𝑦2 = 1I𝑙:𝑥+ 𝑦+ 2 = 0I𝑃¬𝑙-"ď.I›.𝑃É
!𝐶"9Ò+I+.A¶¬𝐴I𝐵I£𝐴𝐵›8.      .
14Y2024·ĻĭƘƙ·ĞģĤĥZī‹!𝐶:𝑥2 + (𝑦−2)2 = 1J!𝐷:𝑥2 + 𝑦2−6𝑥−10𝑦+ 30 = 0IM,N A¶\
! C,D -"ď.IP ¬ x ‚-"ď.I£|𝑃𝑀| + |𝑃𝑁|"6©7\      .
Ó,Kƚ
15Y23-24 Ã-·^ƋƌƍƎ·œŔZī‹!𝐶"GH
𝑥2 + 𝑦2−2𝑥−4𝑦+ 𝑚= 0 
(1)¡𝑦= 𝑥+ 𝑚 ! C ż{:.I< m "ü7ýþz
(2)ª!𝐶IJ𝑙:𝑥+ 2𝑦−4 = 0ĐÂ"()¬2 5iI< m "7
16Y23-24 Ã-·ŐĢƛƜ·œŔZī‹!𝐶Ē›.𝐴(1,1)J𝐵(1,−3)IÚ!¦𝐶€𝑥−𝑦−2 = 0-.
(1)<!𝐶GHz
(2)¡!𝐸"GH¬𝑥2 + (𝑦−1)2 = 1I&'!𝐸 !𝐶"#$%.
      
      
17Y2024 °·TU·ŢţZī‹.𝑃(𝑥,𝑦)\!(𝑥+ 2)2 + 𝑦2 = 1-ŊóM.
(1)< P ./3𝑥+ 4𝑦+ 12 = 0"01"6y7J6©7
(2)<𝑥−2𝑦"6y7J6©7
(3)<
𝑦−2
𝑥−1"6y7J6©7
18Y2024 °·TU·ŢţZ€đ3à´µ%5Iī‹.𝐴(2,3)I𝐵(5,0)I𝑀\đ3^"Mď.IÚ
ØÙ
|𝑀𝐴|
|𝑀𝐵| = 2Iŝ.𝑀"Ċ¬…𝐸.
(1)<…𝐸"GHz
(2)›.𝐵"𝑙 …𝐸“ò𝑃I𝑄9.I¡ △𝑂𝐵𝑃"34\ △𝑂𝐵𝑄"34" 3 ƝI<𝑙"GH
19Y2024·ŮůŰ·ĞģĤĥZī‹!𝐶:𝑥2−𝑚𝑥+ 𝑦2 +2(2−𝑚)𝑦+ 𝑚−1 = 0,𝑚∈R
(1)Ŧŭ
! C ›8.z
(2)ª𝑚= 0iI. P ¬𝑙:
𝑥
6 +
𝑦
3 = 1-"ď.I› P É! C "9Ò+I+.A¶¬ AIBI<Óŏs𝑃𝐴𝐶𝐵
346©7Iŧƞ~ƒi AB "GH