Question

When the origin is shifted to $(2,3)$ the transformed equation $x^2+3xy-2y^2+17x-7y-11=0$ then the original equation of curve is__________

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

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,
$x^2+3xy-2y^2+17x-7y-11=0\text{, }$
to get the original equation of curve, replace $(x,y)$ by $(x-2,y-3)$, so by doing this. we get,
$(x-2{)}^2+3(x-2)(y-3)-2(y-3{)}^2+17(x-2)-7(y-3)-11=0$
$\Rightarrow x^2-4x+4+3(xy-3x-2y+6)-2\left(y^2-6y+9\right)+17x-34-7y+21-11=0$
$\Rightarrow x^2+3xy-2y^2+4x-y-20=0$