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Question

Circles
Number of common tangents
I:x2+y2=4
x2+y28x+12=0
a) 0

II:x2+y2=1
x2+y22x6y+6=0
b) 1

III:x2+y2=16
x2+y28x+6y56=0
c) 4

IV: x2+y22x6y+9=0
x2+y2+6x2y+1=0
d)3


A
a,b,c,d
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B
d,c,b,c
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C
c,b,a,d
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D
d,c,b,a
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Solution

The correct option is A d,c,b,c
I. S1:x2+y2=4 and S2:x2+y28x+12=0
C1(0,0) C2(4,0)
r1=2 r2=2
S1 and S2 Touch each other externally, So no of common tangent are 3.
II. S1:x2+y2=1 and S2:x2+y22x6y+6=0
C1(0,0) C2(1,3)
r1=1 r2=2
C1C2=10 and r1+r2=3
C1C2>r1+r2
S1 & S2 does not intersect each other. So no of common tangents are 4.
III. S1:x2+y2=16 and S2:x2+y28x+6y+56=0
C1(0,0) C2(4,3)
r1=4 r2=9
C1C2=5 and r1+r2=13
r2r1=5
C1C2=r2r1
S1 and S2 Touches internally so no of common tangent are 1.
IV. x2+y22x6x+9=0
C1(1,3)
r1=1
x2+y2+6x2y+1=0
C2(3,1)
r2=3
C1C2>r1r2
S1 and S2 are not intersection so, no of common tangent is 4.
So, d,c,b,c

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