Given the equation `4x^2+2sqrt(3)x y+2y^2=1` . Through what angle should the axes be rotated so that the term `x y` is removed from the transformed equation.

Transform the equation x^(2)+xy-3x-y+2=0 to parallel axis through the point (1,1).

Transform the equation 3x^(2)+2y^(2)-4x+3y=0 to parallel axes through the point (1,-2).

Transform the equations 2x^(2)+y^(2)-4x+4y=0 to parallel axes through the point (1,-2).

The equation of a curve referred to a given system of axes is 3x^2+2x y+3y^2=10. Find its equation if the axes are rotated through an angle 45^0 , the origin remaining unchanged.

The equation sqrt({(x-2)^2+y^2})+sqrt({(x+2)^2+y^2})=4 represents

If x = 2m, y = 16m-3, what will be the value of m so that the equation y = 5x will be solved?

The equation of the bisector of the acute angle between the lines 2x-y+4=0 and x-2y=1 is

If the lines represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated about the point (sqrt(3),0) through an angle of 15^0 , one in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

The least natural numbers, by which the equation 2x+3y=11 and 3x-4y=8 should be multiplied so that the co-efficients of y in both the equations become equal are

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2