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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.

Text Solution

Verified by Experts

Let `AB` is the rod with length `12` cm. and`P(x,y)` is any point such that,
`AP = 3` cm and `PB = 12-3 = 9` cm
we can draw perpendiculars from `P` to X-axis and Y-axis at point `R` and `Q` respectively.
Then, `PQ = x` and `PR = y`
Please refer to video forthe diagram.
Now, in `Delta PBQ`,
`(PQ)/(PB) = cos theta`
`=>x/9 = cos theta ->(1)`
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