The locus of the mid points of the chords of the circle x2+y2āaxāby=0 which subtend a right angle at (a2,b2) is :
ax+by=0
ax+by=a2+b2
x2+y2−ax−by+a2+b28=0
C=(a2,12),r=12√a2+b2
P = (x, y)
cosπ4=CPr⇒CP2=r2 cos2 π4(x−a2)2+(y−b2)2=a2+b28
The locus of the mid points of the chords of the circle x2+y2−ax−by=0 which subtend a right angle at (a2,b2) is :