Centres and radii of the given circles are C1(0,0),r1=3 and C2(−α,−1) r2=√α2+1−1=|α| Since, two circles touch internally. ∴‌C1C2‌‌=r1−r2 ⇒‌√α2+12‌‌=3−|α| ⇒‌α2+1‌‌=9+α2−6|α| ‌⇒‌6|α|‌‌=8⇒|α|=‌