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

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

A line through the point P (1, 2) makes an angle of 60^0 with the positive direction of x-axis and is rotated about P in the clockwise direction through an angle 15^0 . Find the equation of the straight line in the new position.

A line through the point A(2, 0) which makes an angle of 30^0 with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15^0 . Find the equation of the straight line in the new position.

Let L be the line 2x+y-2=0 . The axes are rotated by 45^@ in clockwise direction then the intercepts made by the line L on the new axes are respectively

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

The line 2x-y = 5 turns about the point on it, whose ordinate and abscissae are equal through an angle of 45^@ in the anti-clockwise direction. Find the equation of the line in the new position.

A line intersects x-axis at point (-2, 0) and cuts off an intercept of 3 units from the positive side of y-axis. Find the equation of the line.

Find the equation to the line which is perpendicular to the line x/(a)-y/(b)=1 at the point where it meets the x-axis.

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 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.