Question

Find the coordinates of the point through which the lines $ax+by+c=0$ pass if $3a+2b+4c=0$.

Answer 1

Equation of the lines is

$ax+by+c=0$ ............. (1)

It is given that,

$3a+2b+4c=0$ .............. (2)

If the lines passes through a point $(h,k)$, then

$ah+bk+c=0$ ............. (3)

Equations (2) and (3) will be true, if

$\frac{h}{3}=\frac{k}{2}=\frac{1}{4}$

$\Rightarrow h=\frac{3}{4}$ and $k=\frac{2}{4}=\frac{1}{2}$