TS EAMCET 14-Sep-2020 Shift 2 Solved Paper

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