If the axes be turned through an angle `tan^-1 2` (in anticlockwise direction), what does the equatio `4xy-3x^2=a^2` become ?

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 angles 30° in the anticlockwise direction and the point is (4, -2 sqrt3) in the new system, the formal point is

The coordinate axes are rotated through an angle theta about the origin in anticlockwise sense. If the equation 2x^(2)+3xy-6x+2y-4=0 change to ax^(2)+2hxy+by^(2)+2g x+2fy+c=0 then a+b is equal to

A point (2,2) undergoes reflection in the x . axis and then the coordinate axe are rotated through an angle of (pi)/(4) in anticlockwise direction.The final position of the point in the new coordinate system is

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