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