Question

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__________

• A. $x^{2}-2 y^{2}-3 x y+4 x-y+20=0$
• B. $x^{2}-2 y^{2}+3 x y+4 x-y-20=0$
• C. $x^{2}-2 y^{2}-3 x y-4 x-y+20=0$
• D. $x^{2}-2 y^{2}-3 x y+4 x-y-20=0$

Answer 1

Answer: (B)

It is given that the origin is shifted to point $(2,3)$ and due to that the transformed equation of the curve is,
$x^{2}+3 x y-2 y^{2}+17 x-7 y-11=0 \text {, }$
to get the original equation of curve, replace $(x, y)$ by $(x-2, y-3)$, so by doing this. we get,
$(x-2)^{2}+3(x-2)(y-3)-2(y-3)^{2}+17(x-2)-7(y-3)-11=0$
$\Rightarrow x^{2}-4 x+4+3(x y-3 x-2 y+6)-2\left(y^{2}-6 y+9\right)+17 x-34-7 y+21-11=0$
$\Rightarrow x^{2}+3 x y-2 y^{2}+4 x-y-20=0$