A 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 $\frac{x}{a}+\frac{y}{b}=1$ meets the axis at A and B

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

Let P ( x, y ) be the point on locus

P( x, y )= mid point of AB

$\begin{array}{l}\Rightarrow \left(x,y\right)=\left(\frac{a+0}{2},\frac{0+b}{2}\right)\\ \Rightarrow x=\frac{a}{2},y=\frac{b}{2}\\ \Rightarrow a=2x,b=2y\\ Givena+b=10\\ \Rightarrow 2x+2y=10\\ \Rightarrow x+y=5\end{array}$