Q. 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
Straight Lines
Solution:
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. $-8x+5y=60$
