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Question

The number of common tangents that can be drawn to the circles x2+y212x+8y+48=0 and x2+y24x+2y4=0 is

A
0
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B
4
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C
2
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D
3
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Solution

The correct option is D 3
x2+y212x+8y+48=0 [ From point (1) ]
r1=2
C1(6,4)
and x2+y24x+2y4=0
C2(2,1)
r23
Distance between centre =42+32
=5=r1+r2
So, This two circle touch each other.
So. no of common tangent =2 external tangents
+1 internal tangent
=3 tangent common,

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