The coordinates of the middle point of the chord cut-off by 2x−5y+18=0 by the circle x2+y2−6x+2y−54=0 are

Given that x2+y2−6x+2y−54=0 ….(1) and 2x−5y+18=0 ….(2) Centre (3,−1) Mid point of the chord=foot of the perpendicular distance from centre to (2).∴h−x1a=k−y1b=−(ax1+by1+c)a2+b2 h−32=k+1−5=−(6+5+18)4+25=−1 h−3=−2⇒h=1, k+1=5⇒k=4 ∴ Mid point=(1,4)