Question

A variable line $\frac{x}{a}+\frac{y}{b}=1$ is such that $a+b=4$. The locus of the midpoint of the portion of the line intercepted between the axes is

• A. $x+y=4$
• B. $x+y=8$
• C. $x+y=1$
• D. $x+y=2$

Answer 1

The correct option is D $x+y=2$

$\frac{x}{a}+\frac{y}{b}=1$ is the equation of line.

intersection with x-axis at $(a,0)$, $y=0$

intersection with y-axis at $(0,b)$, $x=0$

Mid point of portion of segment $(a,0)$ and $(0,b)$ is $(x,y)=(\frac{a+0}{2},\frac{0+b}{2})=(\frac{a}{2},\frac{b}{2})$

As $a+b=4$

$\Rightarrow 2x+2y=4$

$\Rightarrow x+y=2$