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