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

The correct option is 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

$\therefore -4=\frac{5\times 0+3\times \alpha }{5+3}$ and $3=\frac{5\times b+3\times 0}{5+3}$

$\Rightarrow a=\frac{-32}{3}$ and $b=\frac{24}{5}$

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

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

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

$\Rightarrow -9x+20y=96$

$\Rightarrow 9x-20y+96=0$