If the origin is shifted to $(2,3)$ and the axes are rotated through an angle $45^{\circ}$ about that point,…
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
$x^2-7 y^2-14 x y-2=0$
$x^2+y^2=4$
$x^2-y^2=4$
$8 x^2-2 y^2=9$
Solution
Given, equation is
$
\begin{array}{rlrl}
& & 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
\end{array}
$
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 $x^2+y^2=4$. Hence, option (b) is correct