Q. 185.0( 3 Votes )

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 x - axis.

Answer :

Given that we need to find the locus of the point on the rod whose ends always touching the coordinate axes.



We need to the equation of locus of point P on the rod, which is 3 cm from the end in contact with x - axis.


Let us assume AB be the rod of length 12 cm and P(x,y) be the required point.


From the figure using similar triangles DAP and CBP we get,




q = 3y ..... (1)




..... - (2)


Now OB = OC + CB



.... (3)


OA = OD + DA


OA = y + 3y


OA = 4y .... (4)


Since OAB is a right angled triangle,


OA2 + OB2 = AB2






x2 + 9y2 = 81


The equation of the ellipse is x2 + 9y2 = 81.


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