Sliding -Stick Problem
In the figure shown, a red stick is sliding smoothly against a wall along the floor.
(You can assume this to be the X-Y Axis as shown in the figure)
It travels from a vertical position to a horizontal position.
If the length of the stick is 2 meters, what is the locus of the blue dot which you see at the center of the stick?
Express this locus as an equation in and .
What is the area under this locus?
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1 solution
Let ends of stick be A(x,0) & B(0,y) such that OA=x & OB=y
As length of stick is constant AB=2, we get
x²+y²=2²=4
Now centre of stick has coordinates (x/2,y/2)
(x/2)²+(y/2)²=1
Locus of centre of stick is a circle of radius 1
Since stick lies in 1st quadrant, area under the quadrant = (pi)x1²/4=3.14/4=0.785