Circles are drawn on the chords of rectangular hyperbola xy = 4 parallel to line y = x as diameters. All such circles pass through two fixed points whose coordinates are

Circles are drawn.........  The circle with points 2t1,2/t1 and 2t2,2/t2 as diameter is x−2t1x−2t2+y−2/t1y−2/t2=0 Also slope −1t1t2=1 t1t2=−1 So equation of circle will become x2+y2−8−t1+t2(x−y)=0 which is of form S+λL=0 so two fixed points are intersection points of (x−y)=0 and x2+y2=8(2,2)&(−2,−2)