If the origin is shifted to remove the first degree terms from the equation 2 x^2-3 y^2+4 x y+4 x+4 y-14=0 then, with respect to this new co-ordinate system, the transformed equation of x^2+y^2-3 x y+4 y+3=0 is

Step-by-step solution

2 x^2-3 y^2+4 x y+4 x+y-14=0 Let x= X +h, y= Y +k Then 2( X + h )^2-3( Y +k)^2+4( X + h )( Y +k)+4( X + h )+4( Y +k)-14=02 X ^2-3 Y ^2+4 XY +(4+4 h+4 k) X +(4-6 k+4 h) Y +2 h^2-3 k^2+4 h k+4 h+4 k-14=0 To remove first degree terms aligned & 4+4 h+4 k=0 and 4-6 k+4 h=0 & k=0, h=-1 & x= X -1, y= Y aligned Now, transformation of x^2+y^2-3 x y+4 y+3=0 is aligned & ( X -1)^2+ Y ^2-3( X -1) Y +4 Y +3=0 & X ^2+ Y ^2-3 XY -2 X +7 Y +4=0 aligned