Find the centre of the conic
`14x^2-4xy+11y^2-44x-58y+71=0`

Options

A. (2, 3)
B. (-2, 3)
C. (3, 2)
D. none of these

Answer

A

Explanation

Let `S-=14x^(2)-4xy+11y^(2)-44x-58y+71=0` be the given conic, Then,
`(delS)/(delx)=0" and "(delS)/(dely)=0`
`rArr" "28x-4y-44=0" and "22y-4x-58=0`
`rArr" "7x-y-11=0" and "2x-11y+29=0`
Solving these two equations, we get x = 2 and y = 3.
Hence, the coordinates of the centre of the given conic are (2, 3).