If the pair of lines `sqrt(3)x^2-4x y+sqrt(3)y^2=0` is rotated about the origin by `pi/6` in the anticlockwise sense, then find the equation of the pair in the new position.

If the pair of straight lines a x^2+2h x y+b y^2=0 is rotated about the origin through 90^0 , then find the equations in the new position.

If the pair of straight lines a x^2+2h x y+b y^2=0 is rotated about the origin through 90^0 , then find the equations in the new position.

If the pair of straight lines a x^2+2h x y+b y^2=0 is rotated about the origin through 90^0 , then find the equations in the new position.

The line 3x - 4y + 7 = 0 is rotated through an angle pi/4 in the clockwise direction about the point (-1, 1) . The equation of the line in its new position is

The line P Q whose equation is x-y=2 cuts the x-axis at P ,a n dQ is (4,2). The line P Q is rotated about P through 45^0 in the anticlockwise direction. The equation of the line P Q in the new position is y=-sqrt(2) (b) y=2 x=2 (d) x=-2

The plane x-2y+3z=0 is rotated through a right angle about the line of intersection with the plane 2x+3y-4z-5=0, find the equation of the plane in its new position.

Two lines represented by the equation. x^2-y^2-2x+1=0 are rotated about the point (1,0) , the line making the bigger angle with the position direction ofthe x-axis being turned by 45^@ in the clockwise sense and the other line being turned by 15^@ in the anti-clockwise sense. The combined equation of the pair of lines in their new position 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 ,

A line x-y+1=0 cuts the y-axis at A. This line is rotated about A in the clockwise direction through 75^@. Find the equation of the line in the new position (A) sqrt(3)y + x = sqrt3 (B) sqrt x + y = sqrt3 (C) x + sqrty = 1 (D) sqrt x + y = 1

The line x+ 2y=4 is-translated parallel to itself by 3 units in the sense of increasing x and is then rotated by 30^@ in the clockwise direction about the point where the shifted line cuts the x-axis.Find the equation of the line in the new position