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

Since, the line intersects X and Y -axes respectively at A(x-0) and B(0,y)
$-4=\frac{5\times 0+3x}{5+3}$
$\Rightarrow -4=\frac{3x}{8}\Rightarrow x=\frac{-32}{3}$
and $3=\frac{5.y+3.0}{5+3}\Rightarrow 3=\frac{5y}{8}\Rightarrow y=\frac{24}{5}$
Since, the intercept on the X and Y-axes respectively are a = $\frac{-32}{3}andb=\frac{24}{5}$.
$\therefore$ Equation of required line is
$\frac{x}{-\frac{32}{3}}+\frac{y}{-\frac{24}{5}}=1\Rightarrow \frac{-3x}{32}+\frac{5y}{24}=1\Rightarrow -9x+20y=96\Rightarrow 9x-20y+96=0$