Sliding -Stick Problem

Geometry Level 2

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 \(x\) and \(y\).

What is the area under this locus?


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