Question

The equation of the straight line, the portion of which intercepted between the coordinate axes being divided by the point $(-5,4)$ in the ratio $1:2$, is

• A. $8x+5y=60$
• B. $8x-5y=60$
• C. $-8x+5y=60$
• D. None of these

Answer 1

Answer: (C)

Let the equation of the line be $\frac{x}{a}+\frac{y}{b}=1$.
So, the coordinates of A and B are $\left(a,0\right)$ and $\left(0,b\right)$ respectively. Since the point $\left(-5,4\right)$ divides AB in the ratio $1:2$
$\therefore -5=\frac{1.0+2.a}{1+2}$
and $4=\frac{1.b+2.0}{2+1}\Rightarrow a=-\frac{15}{2}$ and $b=12$
So the line is $-\frac{2}{15}x+\frac{y}{12}=1$, i.e. $-8x+5y=60$