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(B) Let the coordinates of the ends of the stick on the floor and the wall be $(a, 0)$ and $(0, b)$ respectively.Since the length of the stick is $10$

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$x^2 + y^2 = 25$

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(B) Let the coordinates of the ends of the stick on the floor and the wall be $(a, 0)$ and $(0, b)$ respectively.Since the length of the stick is $10$ units,by the distance formula,we have $a^2 + b^2 = 10^2 = 100$ --- $(1)$.Let $M(h, k)$ be the middle point of the stick.Using the midpoint formula,$h = \frac{a + 0}{2} = \frac{a}{2}$ and $k = \frac{0 + b}{2} = \frac{b}{2}$.This implies $a = 2h$ and $b = 2k$.Substituting these values into equation $(1)$,we get $(2h)^2 + (2k)^2 = 100$.$4h^2 + 4k^2 = 100$.Dividing by $4$,we get $h^2 + k^2 = 25$.Replacing $(h, k)$ with $(x, y)$,the locus of the middle point is $x^2 + y^2 = 25$.

$A$ stick of length $10$ units rests against the floor and a wall of a room. If the stick begins to slide on the floor,then the locus of its middle point is:

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