Question

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 :

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

Answer 1

Answer: (B)

$x^2+y^2=25$

Let mid point of Rod be $(h,k)$

then coordinates of $A$ and $B$

$\Rightarrow A\equiv (0,2k)$ $B\equiv (2h,0)$

Distance from $A$ to $B\to AB$= fixed (i.e length of rad is fixed)

$\sqrt{(2k{)}^2+(2h{)}^2}=10$

$4(k^2+h^2)=100$

$k^2+h^2=25$

expressing it in a form of locus $x^2+y^2=25$