If $(a,-2 a), a>0$ is the midpoint of a line segment intercepted between the co-ordinate axes, then the…
If $(a,-2 a), a>0$ is the midpoint of a line segment intercepted between the co-ordinate axes, then the equation of the line is
$x-2 y+4 a=0$
$2 x-y=4 a$
$x-2 y=5 a$
$2x-y+4 a=0$
Solution
Given point $(a,-2 a)$ is the midpoint of the intercepts.
Let Points $A, B, M$ be as shown in figure.
Hence the intercept points are $(2 \mathrm{a}, 0)$ and $(0,-4 \mathrm{a})$
Equation of line from intercept in intercept form.
$\frac{x}{2 a}+\frac{y}{-4 a}=1 \Rightarrow 2 x-y=4 a$
