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

$\text{The equation of the given line is,}\frac{x}{a}+\frac{y}{b}=1\text{It cuts the axes at A(a, 0) and B(0, b) The portion of AB intercepts between the axis is 5 : 3}.\therefore h=\frac{3\times a+5\times 0}{8}and\frac{3\times 0+5\times b}{8}\Rightarrow p=(\frac{3a}{8},\frac{5b}{8})\text{The line is passing through the point (-4, 3)}\Rightarrow \frac{3a}{8}=-4\frac{5b}{8}=3\Rightarrow a=\frac{-32}{3}b=\frac{24}{5}\therefore \text{The equation of the given line is},\frac{x}{\frac{-32}{3}}+\frac{y}{\frac{24}{5}}=1\frac{-3x}{32}+\frac{5y}{24}=19x-20y+96=0$