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

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 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

The line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15^@ . find the equation of line in the new position. If B goes to C in the new position what will be the coordinates of C.

If the lines 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 , one 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 pair of straight lines drawn through the origin form with the line 2x+3y=6 an isosceles triangle right - angled at the origin . Find the equations of the pair of the straight lines and the area of the triangle correct to two places of decimals.

A straight line through the point (2,2) intersects the lines sqrt(3)x+y=0 and sqrt(3)x-y=0 at the point A and B , respectively. Then find the equation of the line A B so that triangle O A B is equilateral.

The plane 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane 5x+3y+10 z=25. The equation of the plane in its new position is x-4y+6z=k where k is

If the pairs of lines x^(2)+2xy+ay^(2)=0andax^(2)+2xy+y^(2)=0 have exactly one line in common then the joint equation of the other two lines is given by

Find the equation of the straight line equidistant from the point (2,-2) and the line 3x-4y+1=0.