The correct option is B 4
Given circles are
S1:x2+y2−2x−4y=0 and S2:x2+y2−8y−k=0
Now, the centre and radius of the circles are
C1=(1,2), r1=√5C2=(0,4), r2=√16+k
For the square root to be defined,
16+k≥0⇒k≥−16
Now,
C1C2=√12+22=√5
As both the circles touches internally, so
C1C2=|r1−r2|⇒√5=|√5−√16+k|⇒√5−√16+k=±√5⇒−√16+k=−√5±√5⇒−√16+k=−2√5,0⇒k=−16,4
Hence, from the given options k=4.