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.

The line 2x-y=3 is rotated through an angle (pi)/(4) in anticlockwise direction about the point (2,1) ,then equation of line in its 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

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

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

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