The variable line $\frac{x}{a}+\frac{y}{b}=1$ is such that $a+b=10$. The locus of the midpoint of the portion of the line intercepted between the axes is

Let the given line cuts the $x-$axis in A and B

$A(a,0),B(0,b)$

Let $P(x_1,y_1)$ is the midpoint of $\overline{AB}$

$x_1=\frac{a}{2},y_1=\frac{b}{2}$

$\Rightarrow a=2x_1,b=2y_1$

Given $a+b=10$

$2x_1+2y_1=10$

$x_1+y_1=5$

Locus of $\text{'}P\text{'}$ is $x+y=5$.