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

Given ratio 5:3

Then, $\frac{5b\times 0+3a\times m}{8m}=-4$

$\Rightarrow -32=3a$

$\Rightarrow a=\frac{-32}{3}$
Similarly,

$\frac{5b\times m+3a\times 0}{8m}=-3$

$\Rightarrow 24=5b$

$\Rightarrow b=\frac{24}{5}$

Then,

$\frac{x}{\frac{-32}{3}}+\frac{y}{\frac{24}{5}}=1$

$\Rightarrow \frac{5y}{24}-\frac{3x}{32}=1$

$\Rightarrow \frac{5y}{3}-\frac{3x}{4}=8$

$\Rightarrow 20y-9x=96$ is the required equation