If the axes are rotated through an angle `theta` without changing the position of the origin,then the transformation is called.

If the origin shifted to another point without changing the directions of axis then the transformation is called

If the axes are rotated through an angle theta in counter clockwise direction, the transformed equation of 4xy-3x^(2)=a^(2) is given by X^(2)-4Y^(2)=a^(2) then positive integer value of tan theta=

If the axes are rotated through an angle theta then the co-ordinates of a point P(x,y) are transformed as P'(X,Y) then X=,Y=

If the origin is shifted to (h,k) and the axes are rotated through an angle theta ,then the co-ordinates of a point P(x,y) are transformed as P(X,Y)=

If the axes are rotated through an angle 180^(@) in the positive direction, the new coordinates of (x,y) are

When axes are rotated through an angle of 45^(@) in positive direction without changing origin then the coordinates of (sqrt(2),4) in old system are

If the axes are rotated through an angle of 45^(@) in the clockwise direction, the coordinates of a point in the new systeme are (0,-2) then its original coordinates are

If the axes are rotated through an angle of 45^(@) in the anti clockwise direction then the equation of rectangular hyperbola x^(2)-y^(2)=a^(2) changes to

Origin shifted to the point (2,-3) without changing the direction of the axes then (-1,2) is transformed as

When the axes of coordinates are rotates through an angle pi//4 without shifting the origin, the equation 2x^(2)+2y^(2)+3xy=4 is transformed to the equation 7x^(2)+y^(2)=k where the value of k is