If are the rotated through an acute angle in clockwise direction about origin so that equation `x^2 + 2xy + y^2 - 2x + 2y = 0` becomes free from xy in its new position, then find equation in new position

The line 3x - 4y + 7 = 0 is rotated through an angle pi/4 in the clockwise direction about the point (-1, 1) . The equation of the line in its new position is

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

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

If the axes are rotated through an angle 30^(0) about the origin then the transformed equation of x^(2) + 2 sqrt(3) xy - y^(2) = 2a^(2) is

The line 3x-4y+7=0 is rotated through an angle (pi)/(4) in the clockwise direction about the point (-1,1). The equation of the line in its new position is

If the line x-y-2=0 is rotated through an angle (pi)/(12) in the clockwise direction about point P(5,3) and equation of line in new position is x-sqrt(3)y+k=0 ,then k is

Find the angle through which the axes be rotated to remove the xy term from the equations x^(2) + 4xy + y^(2) - 2x + 2y - 6 = 0

The line 2x-y=3 is rotated through an angle (pi)/(4) in anticlockwise direction about the point (2,1) ,then equation of line in its new position

If the lines represented by x^(2)-2pxy-y^(2)=0 are rotated about the origin through an angle theta , one clockwise direction and other in anti-clockwise direction, then the equation of the bisectors of the angle between the lines in the new position is