If the origin is shifted to (2,3) and the axes are rotated through an angle 45° about that point, then the transformed equation of 2 x2+2 y2-8 x-12 y+18=0 is

Question

If the origin is shifted to (2,3) and the axes are rotated through an angle 45° about that point, then the transformed equation of 2 x2+2 y2-8 x-12 y+18=0 is (A) x2-7 y2-14 x y-2=0 (B) x2+y2=4 (C) x2-y2=4 (D) 8 x2-2 y2=9

Tardigrade Admin · Accepted Answer

Given, equation is 2 x2+2 y2-8 x-12 y+18=0 ⇒ 2(x-2)2+2(y-3)2=8 ⇒ (x-2)2+(y-3)2=4 After the shifting of origin to (2,3), the transformed equation becomes x2+y2=4 and after the rotation of axes through an angle 45° about the point, the transformed equation is x2+y2=4.

Q. If the origin is shifted to $(2, 3)$ and the axes are rotated through an angle $4 5^{\circ}$ about that point, then the transformed equation of $2 x^{2} + 2 y^{2} - 8 x - 12 y + 18 = 0$ is

$x^{2} - 7 y^{2} - 14 x y - 2 = 0$

$x^{2} + y^{2} = 4$

$x^{2} - y^{2} = 4$

$8 x^{2} - 2 y^{2} = 9$

Q. If the origin is shifted to (2,3) and the axes are rotated through an angle 45∘ about that point, then the transformed equation of 2x2+2y2−8x−12y+18=0 is

x2−7y2−14xy−2=0

x2+y2=4

x2−y2=4

8x2−2y2=9

Given, equation is 2x2+2y2−8x−12y+18=0 ⇒2(x−2)2+2(y−3)2=8 ⇒(x−2)2+(y−3)2=4 After the shifting of origin to (2,3), the transformed equation becomes x2+y2=4 and after the rotation of axes through an angle 45∘ about the point, the transformed equation is x2+y2=4.

Q. If the origin is shifted to $(2, 3)$ and the axes are rotated through an angle $4 5^{\circ}$ about that point, then the transformed equation of $2 x^{2} + 2 y^{2} - 8 x - 12 y + 18 = 0$ is

$x^{2} - 7 y^{2} - 14 x y - 2 = 0$

$x^{2} + y^{2} = 4$

$x^{2} - y^{2} = 4$

$8 x^{2} - 2 y^{2} = 9$