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.


Let AB be the rod making an angle Ɵ with OX and P(x,y) be the point on it such that AP = 3cm.



Then, PB = AB – AP = (12 – 3)cm = 9cm [AB = 12cm]


From P, draw PQ OY and PROX.


In ΔPBQ,



Since, sin2Ɵ +cos2Ɵ = 1,



Or,


Thus, the equation of the locus of point P on the rod is .


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