Question

The equation of the straight line which passes through the point (−4, 3) such that the portion of the line between the axes is divided internally by the point in the ratio 5 : 3 is
(a) 9x − 20y + 96 = 0
(b) 9x + 20y = 24
(c) 20x + 9y + 53 = 0
(d) none of these

Answer 1

(a) 9x − 20y + 96 = 0

Let the required line intersects the coordinate axis at (a, 0) and (0, b).


The point (−4, 3) divides the required line in the ratio 5 : 3

$$\begin{gathered} \therefore -4=\frac{5\times 0+3\times a}{5+3}\mathrm{and}3=\frac{5\times b+3\times 0}{5+3} \\ \Rightarrow a=\frac{-32}{3}\mathrm{and}b=\frac{24}{5} \end{gathered}$$

Hence, The equation of the required line is given below:

$$\begin{gathered} \frac{x}{{\displaystyle \frac{-32}{3}}}+\frac{y}{{\displaystyle \frac{24}{5}}}=1 \\ \Rightarrow \frac{-3x}{32}+\frac{5y}{24}=1 \\ \Rightarrow -9x+20y=96 \\ \Rightarrow 9x-20y+96=0 \end{gathered}$$