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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 3 cm from the end in contact with the x–axis.

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To find 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 Configuration Let the ends of the rod be points A and B, where A is on the x-axis and B is on the y-axis. The length of the rod is 12 cm, so if A is at (x, 0) and B is at (0, y), we have: \[ x + y = 12 \] ### Step 2: Define the Position of Point P Point P is located 3 cm from the end in contact with the x-axis (point A). Therefore, the coordinates of point P can be defined as: ...
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