Question

The equation of the straight line which passes through the point $P(-4,3)$ such that the portion of it between the $x$-axis and $y$-axis is divided by the point $P$ in the ratio $1:2$ respectively, is

• A. $\frac{x}{6}-\frac{y}{9}=1$
• B. $\frac{x}{9}-\frac{y}{6}=1$
• C. $\frac{y}{9}-\frac{x}{6}=1$
• D. $\frac{y}{9}+\frac{x}{6}=1$

Answer 1

The correct option is C $\frac{y}{9}-\frac{x}{6}=1$


Let the required line be $\frac{x}{a}+\frac{y}{b}=1$

Using section formula, we get the coordinates of $P$
$(-4,3)=(\frac{2a+0}{3},\frac{b+0}{3})\Rightarrow (-4,3)=(\frac{2a}{3},\frac{b}{3})\Rightarrow a=-6,b=9$

So, the equation of the line is
$\frac{x}{-6}+\frac{y}{9}=1\Rightarrow \frac{y}{9}-\frac{x}{6}=1$