By translation of axes the equation `xy-x +2y-6=0` changed as `XY=c` then `c=`

By translating the axes the equation xy-x+2y=6 has changed to xy=c, then c =

By translating the axes the equation xy-2x-3y-4=0 has changed to XY=k, then k=

Separate the equation 5x^2+6xy+y^2=0

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

If the origin is shifted to a point (h, k) by translation of axes in order to make the equation x^(2)+5xy+2y^(2)+5x+6y+7=0 free from first order terms, then

The solution of the differential equation (xy-y)dx+(xy-x)dy=0 is: (where c is the constant of integration)

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

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

The angle of rotation of axes to remove xy term in the equation x^(2) + 4xy + y^(2) - 2x + 2y -6=0 is