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

The circle with points P(2t1,2/t1) and Q(2t2,2/t2) as diameter is given byx−2t1x−2t2+y−2t1y−2t2=1…………..(i)Also, the slope of PQ is given by−1t1t2=1 or t1t2=−1Hence, from (i), the circle isx2+y2−8−t1+t2(x−y)=0which is of the form S+λL=0Hence, circles pass through the points of intersection of the circle x2+y2 -8 = 0and the line x= y.The points of intersection are (2,2) and (-2,-2).