Q : 11        Prove that the line through the point  $(x_1,y_1)$  and parallel to the line   $Ax+By+C=0$   is   $A(x-x_1)+B(y-y_1)=0.$

It is given that line is parallel to the line  $Ax+By+C=0$
Therefore, their slopes are equal
The slope of line $Ax+By+C=0$  , $m'= \frac{-A}{B}$
Let the slope of other line be m
Then,
$m =m'= \frac{-A}{B}$
Now, the equation of the line passing through the point $(x_1,y_1)$  and with slope $-\frac{A}{B}$  is
$(y-y_1)= -\frac{A}{B}(x-x_1)$
$B(y-y_1)= -A(x-x_1)$
$A(x-x_1)+B(y-y_1)= 0$
Hence proved

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