Question

When the axes are translated to the point $(5,-2)$, then the transformed form of the equation $xy+2x-5y-11=0$ is

• A. $\frac{X}{Y}=1$
• B. $\frac{Y}{X}=1$
• C. $XY=1$
• D. $X{Y}^2=2$

Answer 1

Answer: (C)

$XY=1$

Since the axes are translated by $(5,-2)$,

Let $x-5=X$

and $y+2=Y$

Therefore, $x=X+5$
and $y=Y-2$

Hence, $xy+2x-5y-11=0$

$\Rightarrow (X+5)(Y-2)+2(X+5)-5(Y-2)-11=0$

$\Rightarrow XY-2X+5Y-10+2X+10-5Y+10-11=0$

$\Rightarrow XY-10+10+10-11=0$

$\Rightarrow XY-1=0$
$\Rightarrow XY=1$