The centres of the given circles are C1(1,3+√7) and C2(4,3) and corresponding radii are r1=√12+(3+√7)2−(8+6√7)=3 and r2=√42+32−k2=√25−k2 Now, C1C2=√(4−1)2+(3−3−√7)2=4 Clearly, C1C2<r1+r2 ⇒4<3+√25−k2⇒1<√25−k2 ⇒1<25−k2⇒k2<24 ∴k=0,±1,±2,±3,±4[∵k∈Z]