Question

Find the transformed equation of the straight line $xy-x-y+1=0$, when the origin is shifted to the point $(1,1)$ after translation of axes.

• A. $xy=5$
• B. $xy=2$
• C. $xy=0$
• D. $xy=8$

Answer 1

Answer: (C)

Let the coordinates of a point $P$ changes from $(x,y)$ to $(x^{\prime },y^{\prime })$ in new coordinates axes where origin has the coordinates $h=1$,
$k=1$
There, $x=x^{\prime }+1$,
$y=y^{\prime }+1$.
Substituting these values in the given equation of straight line $(x^{\prime }+1)(y^{\prime }+1)-(x^{\prime }+1)-(y^{\prime }+1)+1=0$
$\Rightarrow x^{\prime }{y}^{\prime }+x^{\prime }+y^{\prime }+1-x^{\prime }-1-y^{\prime }-1+1=0$
$\Rightarrow x^{\prime }{y}^{\prime }=0$
Therefore, the equation of straight line in the new systemis $xy=0$