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. $20+9y+63=0$
• D. None of these

Answer 1

Answer: (A)

$9x-20y+96=0$

Let the line cut the $x$ axis at $(a,0)$ and $y-$axis at $(0,b).$
Therefore
It is given that the point $(-4,3)$ divides the line internally in $5:3$ ratio. Hence applying the formula for internal division of line segment, we get
$\frac{3a}{8}=-4$ and $\frac{5b}{8}=3$
Hence $a=\frac{-32}{3}$ and $b=\frac{24}{5}$
Using slope intercept form we get
$\frac{x}{\frac{-32}{3}}+\frac{y}{\frac{24}{5}}=1$
$9x-20y+96=0$