The coordinate axes are rotated through an angle `theta` about the origin in anticlock-wise sense `2x^2 +3xy-6x+2y-4=0` change to `ax^2+2hxy+by^2 +2gx +2fy+c =0` then `a+b` is equal to

the equation ax^(2)+ 2hxy + by^(2) + 2gx + 2 fy + c=0 represents an ellipse , if

The equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents a circle if

The equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 repersents a hyperbola if

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=

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

The principal axes of the hyperbola ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c = 0 are parallel to the lines

circle ax^(2)+ay^(2)+2gx+2fy+c=0 touches X -axis,if