If first degree terms and constant term are to be removed from the equation `12x^(2)+7xy-12y^(2)-17x-31y-7=0` , then the origin must be shifted at shifted at the point .

Options

A. `(1,-1)`
B. `(-1,1)`
C. `(-1,-1)`
D. none of these

Answer

A

Explanation

We have,
`f=12x^(2)+7xy-12y^(2)-17x-31y-7=0`
This equation represents a pair of straight lines. In order to remove the first degree terms and constant term, we must shift the origin at their point of intersection whose coordinates are obtained by solving
`(delf)/(delx)=0 and (delf)/(dely)=0`
i.e. `24x+7y-17=0 and 7x-24y-31=0`
Clearly, x = 1, `y=-1` satisfies these equations.
Hence, the required point is `(1,-1)`.