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. [NCERT EXAMPLE]

Answer 1

The x - coordinate of the point A is given by
$$\begin{gathered} -4=\frac{3\times a+5\times 0}{3+5} \\ \Rightarrow a=\frac{-32}{3} \end{gathered}$$
The y - coordinate of the point B is given by
$$\begin{gathered} 3=\frac{3\times 0+5\times b}{3+5} \\ \Rightarrow b=\frac{24}{5} \end{gathered}$$
The equation of the line passing is given by
$$\begin{gathered} \frac{x}{{\displaystyle \frac{-32}{3}}}+\frac{y}{{\displaystyle \frac{24}{5}}}=1 \\ \Rightarrow 9x-20y+96=0 \end{gathered}$$