If first degree terms and constant term are to be removed from the equation `12x^(2)+7xt-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 the constant term , we must shift the origin at their point of intersection `=((-12xx((-17)/(2))-((-31)/(2)xx(7)/(2))))/(((7)/(2))^2-12xx(-12)),(12xx((-31)/(2))-((-17)/(2))xx(7)/(2))/(((7)/(2))^2+144)`
`=(((204)/(2)+(217)/(4))/((625)/(4)),((-372)/(2)+(119)/(4))/((625)/(4)))=((625)/(625),(-625)/(625))=(1,-1)`