The co-ordinates of the middle point of the chord cut off on 2x - 5y +18= 0 by the circle `x^2 + y^2 - 6x + 2y - 54 = 0` are (A) (1,1) (B) (2, 4) (C) (4,1) (D) (1, 4)

Options

A. `(1,4)`
B. `(2,4)`
C. `(4,1)`
D. `(1,1)`

Answer

A

Explanation

The co-ordinates …………

`2x-5y+18=0` …….(i)
`x^(2)+y^(2)-6x+2y-5=0` ……….(ii)
let mid point be `(h, k)`
`m_(OM)xxm_(AB) = -1`
`((K+1)/(h-3))xx((2)/(5))= -1` and `(h, k)` lies on `2x-5y+18=0`
Hence `2h-2k+18=0` ......(ii)
by (i) and (ii) `(h, k) = (1, 4)`