Given system of circles is x2+y2+4x+7‌=0 . . . (i) 2(x2+y2)+3x+5y+9‌=0 . . . (ii) ‌ or ‌x2+y2+‌
3
2
x+‌
5
2
y+‌
9
2
‌=0 . . . (iii) ‌ and ‌‌x2+y2+y‌=0 The radical centre can be obtained by solving the Eqs. (i), (ii) and (iii). On subtracting Eq. (ii) from Eq. (i), we get 4x−‌
3
2
x−‌
5
2
y+7−‌
9
2
‌=0 ⇒‌
5
2
x−‌
5
2
y+‌
5
2
‌=0 x−y+1‌=0 . . . (iv) On subtracting Eq. (iii) from Eq. (i), we get 4x−y+7=0 . . . (v) On solving Eqs. (iv) and (v), we get and ‌‌y=−1 Hence, radical centre is (−2,−1).