If the coordinate axes are rotated through an angle 6 about the origin, then the transformed equation of 3 x^2-4 x y+ 3 y^2=0 is

Step-by-step solution

Given equation, 3 x^2-4 x y+ 3 y^2=0 Coordinate axes are rotated through an angle of 6 about the origin Now, axis is x 6 y 6 and x 6 +y 6 Thus, equation becomes 3 (x 6 -y 6 )^2 aligned & -4 (x 6 -y 6 ) & (x 6 +y 6 )+ 3 (x 6 +y 6 )^2=0 & 3 ( 3 x 2 - 1 2 y )^2-4 ( 3 x-y 2 ) & ( x+ 3 y 2 )+ 3 ( x+ 3 y 2 )^2=0 & 3 (3 x^2-2 3 x y+y^2 )-4 ( 3 x^2+3 x y-x y- 3 y^2 ) & 3 3 x^2-6 x y+ 3 y^2-4 3 x^2-12 x y & +4 x y+4 3 y^2+ 3 x^2+6 x y+3 3 y^2=0 & 8 3 y^2-8 x y=0 & 3 y^2-x y=0 aligned