Question

Find the equation of the straight line that passes through the point $A(-5,-4)$ and is such that the portion intercepted between the axes is divided by the point A in the ratio $1:2$(internally).

Answer 1

Let the required line intercept the y-axis at $Y(0,k)$ and the x-axis at $X(h,0)$.

Now, it is given that $A$ divides the line $XY$ in ratio $1:2$ internally.

$\therefore 2AX=AY$

$\therefore A=\frac{2X+Y}{3}$

$\therefore (-5,-4)=(\frac{2h+0}{3},\frac{0+k}{3})$

$\therefore (-5,-4)=(\frac{2h}{3},\frac{k}{3})$

$\therefore -5=\frac{2h}{3},-4=\frac{k}{3}$

$\therefore h=-\frac{15}{2},k=-12$

$\therefore$ equation of straight line $XY$ is $\frac{y-(-12)}{x-0}=\frac{0-(-12)}{-\frac{15}{2}-0}$

$⟹\frac{y+12}{x}=-\frac{8}{5}$

$⟹8x+5y+60=0$

This is the required equation of line.