AP EAPCET 19-Aug-2021 Shift 1 Paper

Given, equation of circle
x2+y2+4x+16y−30=0 ...(i)
Comparing with x2+y2+2g1x+2f1y+c1=0
We have, g1=2,f1=8,c1=−30
Let equation of circle whose centre at (1,2) is
x2+y2−2x−4y+c=0 ...(ii)
Here, g2=−1,f2=−2,c2=c
Circles Eqs. (i) and (ii) are orthogonal, then
2(g1g2+f1f2)=c1+c2
⇒2(−2−16)=−30+c
or c=−6
From Eqs. (ii), we get
x2+y2−2x−4y−6=0
Radius =√(−1)2+(−2)2−(−6)=√11