Find the point at which origin is shifted such that the transformed equation of `x^(2)+2y^(2)-4x+4y-2=0` has no first degree term. Also find the transformed equation .

Find a point at which origin is shifted such that transformed equation of x^(2)+xy-3x-y+2=0 has no first degree term and constant term. Also find the transformed equation.

Find the point at which origin is shifted such that the transformed equation of y^(2)-4y+8x-2=0 is independent of constant term.

Find a point at which origin is shifted such that transformed equation of 2x^(2)+y^(2)-12xy+16=0 has no term containing x and constant term.

Find the point at which is shifted such that the transformed equations of the following equations has no first degree term : (i) 2x^(2)+3y^(2)+4x-12y+10=0 (ii) x^(2)+y^(2)-xy-5x+4y+5=0

Find the transformed equation of 2x^(2)+y^(2)-4x+4y=0 when the origin is shifted to the point (-1,2).