Let ‌‌S1:x2+y2=9 and S2:x2+y2+2αx+2y+1=0 Now, centre and radius of S1 are ‌‌ Centre ‌=C1(0,0) ‌‌ Radius ‌=3 Centre and radius of S2 are ‌‌ Centre ‌=C2(−α,−1) ‌‌ Radius ‌=√(−α)2+(−1)2−1=α Since, S1 and S2 touch each other internally, then ‌C1C2=|r2−r1| ⇒√(−α−0)2+(−1−0)2=|α−3| ⇒√α2+1=|α−3| ⇒α2+1=(α−3)2 ⇒α2+1=α2−6α+9 ⇒α2+1=α2−6α+9 ⇒6α=8⇒α=‌