If the axes are rotated through an angle `180^@` then the equation `2x - 3y + 4=0` becomes

If the transformed equation of a curve is X^(2)+2sqrt(3)XY-Y^(2)=2a^(2) ,when the axes are rotated through an angle of 60^(@) ,then the original equation

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

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 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

When the axes rotated through an angle 90^(0) .The equation 5x-2y+7=0 transforms to pX+qY+r=0 Then 2p+q+r=

If the axes are rotated through an angle of 30^(@) in the clockwise direction, the point (4,-2 sqrt3) in the new system was formerly

The transformed equation of 4xy-3x^2=10 when the axes are rotated through an angle whose tangent is 2 is aX ^2 - bY^2=10 then a+b is

If the equation 4x^2+2xy+2y^2 - 1=0 becomes 5X^2+Y^2=1 when the axes are rotated through an angle of t degrees then sum of the digits of t is