When the angle of rotation of axes is `Tan^(-1)2` ,the transformed equation of `4xy-3x^(2)=a^(2)` is

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=

The angle of rotation of axes in order to eliminate xy term in the equation xy=c^(2) is

13.When the axes are rotated through an angle 45^@ , the transformed equation of a curve is 17x^(2)-16xy+17y^(2)=225 .Find the original equation of the curve.

Keeping coordinate axes parallel, the origin is shifted to a point (1, –2), then transformed equation of x^2 + y^2 = 2 is -

The angle of rotation of axes so that sqrt(3)x-y+1=0 transformed as y=k is (i) (pi)/(6)( ii) (pi)/(4)( iii) (pi)/(3)( iv) (pi)/(2)

If the axes are shifted to (-2,-3) and rotated through (pi)/(4) then transformed equation of 2x^(2)+4xy-5y^(2)+20x-22y-14=0 is

if the axes are rotated through 60 in the anticlockwise sense,find the transformed form of the equation x^(2)-y^(2)=a^(2)