When the origin is shifted to \((2,3)\) the transformed equation \(x^2+3 x y-2 y^2+17 x-7 y-11=0\), then the…
When the origin is shifted to \((2,3)\) the transformed equation \(x^2+3 x y-2 y^2+17 x-7 y-11=0\), then the original equation of curve is
\(x^2-2 y^2-3 x y+4 x-y+20=0\)
\(x^2-2 y^2+3 x y+4 x-y-20=0\)
\(x^2-2 y^2-3 x y-4 x-y+20=0\)
\(x^2-2 y^2-3 x y+4 x-y-20=0\)
Solution
It is given that the origin is shifted to point \((2,3)\) and due to that the transformed equation of the curve is,
\(x^2+3 x y-2 y^2+17 x-7 y-11=0\), to get the original equation of curve, replace \((x, y)\) by \((x-2, y-3)\), so by doing this.
we get, \((x-2)^2+3(x-2)(y-3)-2(y-3)^2\)
\(\begin{gathered}
+17(x-2)-7(y-3)-11=0 \\
\Rightarrow x^2-4 x+4+3(x y-3 x-2 y+6)-2\left(y^2-6 y+9\right) \\
+17 x-34-7 y+21-11=0 \\
\Rightarrow x^2+3 x y-2 y^2+4 x-y-20=0
\end{gathered}\)
Hence, option (b) is correct.