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 line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15^(@) , then find the equation of the line in new position.

If a point A(6,8) rotates through an angle 90^o about the origin in the anticlockwise direction ,find the new position of A.

The line P Q whose equation is x-y=2 cuts the x-axis at P ,and Q is (4,2). The line P Q is rotated about P through 45^@ in the anticlockwise direction. The equation of the line P Q in the new position is (A) y=-sqrt(2) (B) y=2 (C) x=2 (D) x=-2

If the 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 , on 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) y^2-x^2+2sqrt(3)x+3=0 (b) y^2-x^2+2sqrt(3)x-3=0 (c) y^2-x^2-2sqrt(3)x+3=0 (d) y^2-x^2+3=0

If the hyperbola x^2-y^2=4 is rotated by 45^0 in the anticlockwise direction about its center keeping the axis intact, then the equation of the hyperbola is x y=a^2, where a^2 is equal to___________

A pair of tangents are drawn from the origin to the circle x^2+y^2+20(x+y)+20=0 . Then find its equations.

Find the area of the triangle formed by the line x+y=3 and the angle bisectors of the pair of lines x^2-y^2+4y-4=0

Find the equation of the bisectors of the anglebetween the lines 4x+3y=5 and x +2y+3=0.