BITSAT 2020 Paper

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