In order to eliminate the first degree terms from the equation `2x^2+4xy+5y^2-4x-22y+7=0`, the point to which origin is to be shifted is-

Options

A. `(1,-3)`
B. `(2,3)`
C. `(2,3)`
D. `(1,3)`

Answer

C

Explanation

Given line is `2x^2+4xy+5y^2-4x-22y+7=0`
Here, `a=2,b=5,c=7,h=2,g=-2,f=-11`
To eliminate first degree term origin is to be shifted to the point `((hf-bg)/(ab-h^2),(gh-af)/(ab-h^2))`
`((-22+10)/(10-4),(-4+22)/(10-4))`
`=(-2,3)`