Question

If the origin is shifted to $(2,3)$ and the axes are rotated through an angle $45^{\circ}$ about that point, then the transformed equation of $2 x^{2}+2 y^{2}-8 x-12 y+18=0$ is

• A. $x^{2}-7 y^{2}-14 x y-2=0$
• B. $x^{2}+y^{2}=4$
• C. $x^{2}-y^{2}=4$
• D. $8 x^{2}-2 y^{2}=9$

Answer 1

Answer: (B)

Given, equation is
$2 x^{2}+2 y^{2}-8 x-12 y+18=0 $
$\Rightarrow 2(x-2)^{2}+2(y-3)^{2}=8$
$\Rightarrow (x-2)^{2}+(y-3)^{2}=4$
After the shifting of origin to $(2,3)$, the transformed equation becomes $x^{2}+y^{2}=4$ and after the rotation of axes through an angle $45^{\circ}$ about the point, the transformed equation is $x^{2}+y^{2}=4$.