We have x2+y2+4y−5=0. Its centre is C1(0,−2), r1=√4+5=3. Let C2(h,k) be the centre of the smaller circle and its radius r2. Then C1C2=4. ⇒√h2+(k+2)2=3+r2=4 ...(1) ⇒r2=1 But k=r2=1 [it touches x -axis ∴ From eq(1),4=√h2+(1+2)2 ⇒16=h2+9⇒h2=7⇒h=±√7 Since h>0 ∴h=√7 Hence, required circle is (x−√7)2+(y−1)2=1