The acute angle `theta` through which the coordinate axes should be rotated for the point `A(2,4)` to attain the new abscissa 4 is given by

The angle through which the coordinates axes be rotated so that xy-term in the equation 5x^(2)+4sqrt(3)xy+9y^(2)=0 may beb missing, is

The angle through which the axes be rotated so as to remove the term containing xy in the equation 7x^(2)-4xy+4y^(2)=5 is

If the coordinates of two points are A(3,4) and B(-2,5), then find the value of (abscissa of A) - (abscissa of B).

If origin is shifted to the point (2,3) and the axes are rotated through an angle pi//4 in the anticlokwise direction, then find the coordinates of the point (7, 11) in the new system of coordinates.

If the axes are rotated through an angle of 30^(@) in the clockwise direction, the point (4,-2 sqrt3) in the new system was formerly

Two sides of a triangle are parallel to the coordinate axes. If the slopes of the medians through the acute angles of the triangle are 2 and m , the m= 1/2 (b) 2 (c) 4 (d) 8

If the axes are rotated through an angle theta then the co-ordinates of a point P(x,y) are transformed as P'(X,Y) then X=,Y=

The area of the triangle formed by the line passing through through the points (3,4),(5,6) with coordinate axes is