Equation of curves are, x2+y2+gx+c=0 and x2+y2+2fy−c=0 Subtract Eq. (i) from Eq. (ii), we get 2fy−gx=2c⇒‌
2fy−gx
2c
=1 Homogeneousing the Eq. (i), we get x2+y2+gx‌
(2fy−gx)
2c
+‌
C(2fy−gx)2
4c2
=0 ⇒4c(x2+y2)+4gfxy−2g2x2+4f2y2+g2x2 ⇒(4c−2g2+g2)x2+(4c+4f2)y2=0 −4gfxy=0 ∴ A pair of straight formed right angle, then 4c−g2+4f2+4c‌‌=0 g2−4f2‌‌=8c