Q.

There are two circles whose equations are x2+y2=9 and x2+y2−8x−6y+n2=0, n∈Z.  If the two circles have exactly two common tangents then the number of possible values of n  is

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a

2

b

8

c

9

d

None of these

answer is C.

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Detailed Solution

For x2+y2=9, the centre=(0,0)  and the  radius=3. For x2+y2−8x−6y+n2=0, The centre=(4,3)  and the radius=42+32−n2 ∴     42+32−n2>0   0r   n2<52    or   −5d. ∴      3+25−n2>42+32     or   25−n2>2    or  25−n2>4 ∴      n2>21     or    −21
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