Find the equation of the straight line passing through the origin and bisecting the portion of the line `a x+b y+c=0` intercepted between the coordinate axes.

Explanation

Line equation passing through origin is `y=mx`.

Let line `ax+by+c=0` meet the axes at A and B.

So, A`=(-\frac{c}{a},0)`and B`=(0,-\frac{c}{b})`.

Midpoint of AB `=(-\frac{c}{2a},-\frac{c}{2b})`.

Midpoint lies on the line `y=mx`

Therefore, `-\frac{c}{2b}=m\times-\frac{c}{2a}`

`\implies m=\frac{a}{b}`

Thus, the required equation is `y=\frac{a}{b}x` , i.e. `\implies ax-by=0`