When the origin is shifted to the point (2. 3) and then the coordinate axes are rotated through an angle (π/3) in the counter clockw ise sense, then the transformed equation of 3x2 + 2xy + 3y2 -18x -22y + 50 = 0 is

Question

When the origin is shifted to the point (2. 3) and then the coordinate axes are rotated through an angle (π/3) in the counter clockw ise sense, then the transformed equation of 3x2 + 2xy + 3y2 -18x -22y + 50 = 0 is (A) 3x2 + 3y2 - 1 = 0 (B) ( 6 + √3 )x2 - 2xy + (6 - √3 )y2 - 2 = 0  (C) 4x2 + 2y2 - 1 = 0  (D) ( 6 - √3 )x2 + (6 - √3 )y2 + 2xy = 0

Tardigrade Admin · Accepted Answer

Correct answer is (b) ( 6 + √3 )x2 - 2xy + (6 - √3 )y2 - 2 = 0

Q. When the origin is shifted to the point (2. 3) and then the coordinate axes are rotated through an angle $\frac{π}{3}$ in the counter clockw ise sense, then the transformed equation of $3 x^{2} + 2 x y + 3 y^{2} - 18 x - 22 y + 50 = 0$ is

$3 x^{2} + 3 y^{2} - 1 = 0$

$(6 + 3) x^{2} - 2 x y + (6 - 3) y^{2} - 2 = 0$

$4 x^{2} + 2 y^{2} - 1 = 0$

$(6 - 3) x^{2} + (6 - 3) y^{2} + 2 x y = 0$

Correct answer is (b) $(6 + 3) x^{2} - 2 x y + (6 - 3) y^{2} - 2 = 0$

Q. When the origin is shifted to the point (2. 3) and then the coordinate axes are rotated through an angle 3π​ in the counter clockw ise sense, then the transformed equation of 3x2+2xy+3y2−18x−22y+50=0 is

3x2+3y2−1=0

(6+3​)x2−2xy+(6−3​)y2−2=0

4x2+2y2−1=0

(6−3​)x2+(6−3​)y2+2xy=0