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.

Question

Philoid · Accepted Answer

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 .