The co-ordinates of the mid-point of the chord cut off by theline 2 x-5 y+18=0 by the circle x²+y²-6 x+2 y-54=0 are

Step-by-step solution

Let A B be the chord Let the mid point of chord be M ( h , k ) Here centre is O =(3-1) Here O M A B ( slope of OM )( slope of AB )=-1 ( k +1 ~h -3 ) ( 2 5 )=-1 5 ~h +2 k =13 Point M(h, k) lies on the 2 x-5 y+18=0 ...(1) 2 ~h -5 k =-18 ...(2) Solving equation (1) & (2) we get h =1, k =4 (1,4) is required point.