Question

A stick of length $10$ units rests against the floor and a wall of a room. If the stick begins to side on the floor than the locus of its middle point is?

• A. $x^2+y^2=2.5$
• B. $x^2+y^2=25$
• C. $x^2+y^2=100$
• D. None

Answer 1

The correct option is B $x^2+y^2=25$

REF.Image

Let AB be the stick and AO be the wall against which the stick is resting. Let M be the mid point of AB AB=10 cm given

Here AM=MB=5 cm

$\angle AOB={90}^{\circ }$ [ walls are perpendicular to the floor]

Since AM and MB are constant = 5 cm

Therefore the point M forms, the center of the circle, Let (h,k) be the coordinates of point m

Locus of circle will be

$(x-h{)}^2+(y-k{)}^2=(5{)}^2$

Here (h,k)=(0,0)

$(x-0{)}^2+(y-0{)}^2=25$

$x^2+y^2=25$