Question

Prove that the line through the point $(x_1,y_1)$ and parallel to the line $Ax+By+C=0$.

$A(x-x_1)+B(y-y_1)=0$

Answer 1

Given line $Ax+By+C=0$

Slope of given line$=\frac{-A}{B}$

$\therefore$Slope of line parallel to given line$=\frac{-A}{B}$

Required line is passing through $(x_1,y_1)$

$\therefore (y-y_1)=\frac{-A}{B}(x-x_1)$

$B(y-y_1)+A(x-x_1)=0$

$\therefore$Equation of required line is $A(x-x_1)+B(y-y_1)=0$