For a variable line frac{x}{a} + frac{y}{b} = | vedclass

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(C) Given the equation of the line is $\frac{x}{a} + \frac{y}{b} = 1$ and $a + b = 10$.The line intersects the $x$-axis at $A = (a, 0)$ and the $y$-ax

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$x + y = 5$

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(C) Given the equation of the line is $\frac{x}{a} + \frac{y}{b} = 1$ and $a + b = 10$.The line intersects the $x$-axis at $A = (a, 0)$ and the $y$-axis at $B = (0, b)$.Let the midpoint of $AB$ be $(x, y)$.Then $x = \frac{a + 0}{2} = \frac{a}{2} \implies a = 2x$.And $y = \frac{0 + b}{2} = \frac{b}{2} \implies b = 2y$.Substitute $a$ and $b$ into the given condition $a + b = 10$:$2x + 2y = 10$.Dividing by $2$,we get $x + y = 5$.Thus,the locus of the midpoint is $x + y = 5$.

For a variable line $\frac{x}{a} + \frac{y}{b} = 1$ where $a + b = 10$,find the equation of the locus of the midpoint of the portion of the line intercepted between the coordinate axes.

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