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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
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Verified Answer
The correct answer is:
$x^2+y^2=4$
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.
$$
\begin{array}{rlrl}
& & 2 x^2+2 y^2-8 x-12 y+18 & =0 \\
\Rightarrow & 2(x-2)^2+2(y-3)^2 & =8 \\
\Rightarrow & (x-2)^2+(y-3)^2 & =4
\end{array}
$$
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.
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