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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

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Let the AB lies on axes OX and OY. P(x,y) be a moving point at 3 cm distance from A.

`:." "BP=AB-AP=(12-3)cm=9 cm`
Let `angle(NAP)=angle(MPB)=theta`
In `DeltaPMB," "costheta=(x)/(9)`
In `DeltaAPN," "sintheta=(y)/(3)`
Now, from `cos^(2)theta+sin^(2)theta=1`
`(x^(2))/(81)+(y^(2))/(9)=1" "rArr" "x^(2)+9y^(2)=81`
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