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.

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 a line joining two points (3,0) and (5,2) is rotated about the point (3,0) in counter clockwise direction through an angle 15^@ , Then find the equation of the line in the new position.

If line joining two points (3, 0 ) and (5,2) is rotated about the point (3,0) in counter clockwise direction through an angle 15^@ , then the equation of the line 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 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

The plane ax + by = 0 is rotated about its line of intersection with the plane z = 0 through an angle alpha . Prove that the equation of the plane in its new position is ax + by +- (sqrt(a^2 + b^2) tan alpha)z = 0

Consider points A(sqrt13,0) and B(2sqrt13,0) lying on x-axis. These points are rotated anticlockwise direction about the origin through an angle of tan^-1(2/3) . Let the new position of A and B be A' and B' respectively. With A' as centre and radius 2sqrt13/3 a circle C_1 is drawn and with B' as centre and radius sqrt13/3 circle C_2 , is drawn. The radical axis of C_1 and C_2 is