UPSEE Solved Model Paper 7

Equation of circle is x2+y2+2gx+2fy+c = 0
(1 , t) ⇒ 1 + t2 + 2g + 2ft + c = 0 ... (i)
(t , t) ⇒ t2+t2 + 2gt + 2ft + c = 0 ... (ii)
(t , 1) ⇒ 1 + t2 + 2gt + 2f + c = 0 ... (iii)
Subtracting (ii) from (i),
1 + 2g - t2 - 2gt = 0
⇒ 1 - t2 + 2g (1 - t) = 0
⇒ (1 - t) (1 + t + 2g) = 0
⇒ t = 1
∴ one point (t , t)
∴ passes through (1 , 1)