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Q.
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
Let the coordinate of mid point of $AB$ is $(x_1, y_1)$ .
$\therefore \; x_1 = \frac{a+0}{2} , y_1 = \frac{0+b}{2}$
$\Rightarrow \; a = 2x_1 , b = 2y_1$
Given , $a+b=4 $
$\therefore \; 2x_1 + 2y_1 = 4 $
$\Rightarrow \; x_1 + y_1 = 2$
Hence, the locus of the mid point is
$x+ y = 2 $
