Question

Find the equation of the line which passes through the point $(-4,3)$ and the portion of the line intercepted between the axes is divided internally in the ratio $5:3$ by this point.

Answer 1

Let point on $x-$axis be $(x,0)$

$y-$axis be $(0,y)$

$(-4,3)$ divides in $1:3$ ratio

$\Rightarrow =-4=\frac{5x+3\left(0\right)}{5+3}3=\frac{5\left(0\right)+3y}{5+3}$

$\Rightarrow x=-\frac{32}{y}y=8$

So the equation $\frac{5x}{-}32+\frac{4}{8}=1$

$\Rightarrow 5x-4y=-32$