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.

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.

If the 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 , on 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 (a) y^2-x^2+2sqrt(3)x+3=0 (b) y^2-x^2+2sqrt(3)x-3=0 (c) y^2-x^2-2sqrt(3)x+3=0 (d) y^2-x^2+3=0

Find the equation of tangents to hyperbola x^(2)-y^(2)-4x-2y=0 having slope 2.

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

The equation sqrt((x+4)^2+(y+2)^2)+sqrt((x-4)^2+(y-2)^2)=8 represents a

If theta is the angle between the lines given by the equation 6x^2+5x y-4y^2+7x+13 y-3=0 , then find the equation of the line passing through the point of intersection of these lines and making an angle theta with the positive x-axis.

Find the equation to which the equation x^2+7x y-2y^2+17 x-26 y-60=0 is transformed if the origin is shifted to the point (2,-3), the axes remaining parallel to the original axies.

Find the equation of a line passing through the point of intersection of the lines 4x+7y-3=0 and 2x-3y+1=0 that has equal intercepts on the axes.

What does the equation 2x^2+4x y-5y^2+20 x-22 y-14=0 become when referred to the rectangular axes through the point (-2,-3) , the new axes being inclined at an angle at 45^0 with the old axes?