The angle of rotation of axes to remove xy term in the equation `9x^(2) + 2sqrt(3)xy + 7y^(2)=10` is

The angle of rotation of axes to remove xy term in the equation x^(2) + 4xy + y^(2) - 2x + 2y -6=0 is

Find the angle of rotation to eliminate xy term in the equation x^(2)+2sqrt3xy-y^(2)=18.

Find the angle through which the axes be rotated to remove the xy term from the equation ax^(2)+2hxy+ay^(2) = 0

The angle through which the coordinates axes be rotated so that xy-term in the equation 5x^(2)+4sqrt(3)xy+9y^(2)=0 may beb missing, is

Though what angle should the axes be rotated so that the equation 9x^2 -2sqrt3xy+7y^2=10 may be changed to 3x^2 +5y^2=5 ?

The lines represented by the equation x^2 + 2sqrt(3)xy + 3y^(2) -3x -3sqrt(3)y -4=0 , are

Find the point to which the axes are to be translated to eliminate x and y terms (remove first degree terms) in the equation 2x^(2)+4xy+5y^(2)-4x-22y+7 = 0.

By rotating the coordinates axes through 30^(@) in anticlockwise sense the eqution x^(2)+2sqrt(3)xy-y^(2)=2a^(2) change to

Show that if the axes be turned through 7(1^(@))/(2) , the equation sqrt(3)x^(2)+(sqrt(3)-1)xy-y^(2)=0 become free of xy in its new form.

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 .