Question

what does the equation xy-x-y+1=0 becomes if origin is shifted the to (1,1)

Answer 1

$Given \: equation : xy - x - y + 1 = 0$

/* We know that ,

If ( x,y ) are the Coordinates of a point and the Origin is shifted to (h,k) , without changing the orientation of the axes , then the new coordinates ( X , Y ) of the point will be given x = X + h and y = Y + k :

$Here,Origin \: shifted \: to \: ( h , k ) = ( 1 , 1 )$

$Now, \: x = X + 1 ,\: y = Y + 1$

The New equation hence becomes ;

$(X+1)(Y+1) - (X+1) - (Y+1) + 1 = 0$

$\implies XY + X + Y + 1 - X - 1 - Y - 1 + 1 = 0$

$\implies XY = 0$

Therefore.,

$\red { New \: equation : }$

$\green { \: XY = 0}$

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