Question

The equation $XY=1$ is the new form of the equation $xy-3x+2y-7=0$, when the origin is shifted to the point $Q$. Find the co-ordinates of the point $Q$.

Answer 1

$xy-3x+2y-7=0$

$\Rightarrow x(y-3)+2y-6-1=0$

$\Rightarrow x(y-3)+2(y-3)=1$

$\Rightarrow (x+2)(y-3)=1$ …………..$\left(1\right)$ original equation

$xy=1$ ……….$\left(2\right)$ Transformed equation

Let $Q=(a,b)$

If origin is shifted to (a, b)

$X=x-aandY=y-b$ …………….$\left(3\right)$

Put $\left(3\right)$ in $\left(1\right)$

We get $(x+a+2)(y+b-3)=1$

but the final equation should be $XY=1$

on company, we have

$a+2=0$ and $b-3=0$

$\Rightarrow a=-2$ and $b=3$

$\therefore CoordinatesofQare(-2,3)$.