The given two circles are 2x2+2y2−3x+6y+k=0 ⇒ x2+y2−
3
2
x+3y+
k
2
=0...(i) and x2+y2−4x+10y+16=0...(ii) Since, general equation of circle is x2+y2+2‌gx+2‌fy+c=0...(iii) Therefore, comparing eqs. (i) and (ii) with eq. (iii), we get g1=−
3
4
,f1=
3
2
,c1=
k
2
and g2=−2,f2=5,c2=16 Both the circles cut orthogonally, ∴ 2(g1g2+f1f2)=c1+c2 ⇒ 2(