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A rod of length 12 cm moves with its end...

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point `P` on the rod, which is 3cm from the end in contact with the x-axis.

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To determine the equation of the locus of point \( P \) on a rod of length 12 cm that moves with its ends always touching the coordinate axes, we can follow these steps: ### Step 1: Understand the setup The rod has a fixed length of 12 cm and touches both the x-axis and y-axis. Let the point where the rod touches the x-axis be \( (x, 0) \) and the point where it touches the y-axis be \( (0, y) \). The length of the rod gives us the relationship: \[ x + y = 12 \] ...
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