AP EAPCET 19-Aug-2021 Shift 2 Paper

Let equation of circle be
x2+y2+2gx+2fy+c=0 ...(i)
This circle is orthogonal to
x2+y2−2x+3y−7=0 ...(ii)
x2+y2+5x−5y+9=0 ...(iii)
x2+y2+7x−9y+29=0 ...(iv)
By condition of orthogonalty, we have
−2g+3f=c−7 ...(vi)
5g−5f=c+9 ...(vii)
7g−9f=c+29 ...(viii)
from Eq. (vii) c=5g−5f−9
From Eqs. (vi) and (vii), we get
−7g+8f=−16
and g−2f=10
{on subtracting Eq. (vii) from Eq. (viii) }
On solving, we have g=−8,f=−9,c=−4
Required equation of circle.
∴x2+y2−16x−18y−4=0