S‌=x2+y2+2kx+4y−3=0 C1‌=(−k,−2)‌ radius ‌r1=√k2+4+3 S′‌=x2+y2−4x+2ky+9=0 C2‌=(2,−k)‌ radius ‌=√4+k2−9 ‌=√k2−5 Now, angle between two circles S=0 and S′=0 is cos(180∘−θ)=‌
(r12+r22−(d2).
2r1r2
where r1,r2 are the radii and d is the distance between their centres. ‌=‌
Centre of S′=0 lies in I quadrant [∴k=−3] Now, radical axis of S=0 and S′=0 is ⇒‌‌‌x(2k+4)+y(4−2k)−12=0\‌−2x+10y−12=0\‌x−5y+6=0