Q. 43.7( 7 Votes )

A rod of length 15 cm moves with its ends always touching the coordinate axes. Find the equation of the locus of a point P on the rod, which is at a distance of 3 cm from the end in contact with the x-axis.

Answer :

Given: A rod of length 15 cm moves with its ends always touching the coordinate axes. A point P on the rod, which is at a distance of 3 cm from the end in contact with the x-axis


Need to find: Find the equation of the locus of a point P



Here AB is the rod making an angle with the x-axis.


Here AP = 3.


PB = AB – AP = 12 – 3 = 9 cm


Here, PQ is the perpendicular drawn from the x-axis and RP is the perpendicular drawn from y-axis.


Let, the coordinates of the point P is (x, y).


Now, in the triangle BPQ,


cos =


And in the triangle PAR,


sin =


We know, sin2 + cos2 = 1



This is the locus of the point P.


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