Question

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

Answer 1

Equation of the line parallel to line

Ax + By + C = 0 is Ax + By + K = 0 ...(i)

Since line (i) passes through $(x_1,y_1)$

$A{x}_1+B{y}_1+K=0$ . . . (ii)

Subtracting (ii) from (i), we have

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