Circle x2+y2−2x−4y+4=0 ⇒(x−1)2+(y−2)2=1 Centre :(1,2) radius =1 line 3x+4y−k=0 intersects the circle at twodistinct points. ⇒ distance of centre from the line < radius ⇒|
3×1+4×2−k
√32+42
|<1 ⇒|11−k|<5 ⇒6<k<16 ⇒k∈{7,8,9,....15} since k∈I Number of K is 9