When the axes are rotated through an angle `45^@`, the transformed equation of a curve is `17x^2-16xy+17y^2=225`. Find the original equation of the curve.

Find the transformed equation of the curve y^(2)-4x+4y+8=0 when the origin is shifted to (1,-2) .

Find the transformed equation of the curve : x^(2)+y^(2)+4x-6y+16=0 when the origin is shifted to the point (-2,3) .

When the angle of rotation of axes is Tan^(-1)2 ,the transformed equation of 4xy-3x^(2)=a^(2) is

if the axes are rotated through 60 in the anticlockwise sense,find the transformed form of the equation x^(2)-y^(2)=a^(2)

On shifting the origin to the point (1,-1) , the axes remaining parallel to the original axes, the equation of a curve becomes : 4x^(2)+y^(2)+3x-4y+2=0 . Find its original equation.

When the axes are translated to the point (5,-2) then the transformed form of the equation xy+2x-5y-11=0 is

Transform to axes inclined at 45^(@) to the original axes for the equation 17x^(2)-16xy+17y^(2)=225 is