# 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

**Solution:**

Let AB = 12 cm be the rod making an angle θ with OX and P (x, y) be the point on it such that AP = 3 cm.

Then,

PB = AB - AP

= (12 - 3) cm

= 9 cm

From P, draw PQ ⊥ OY and PR ⊥ OX.

In ΔPBQ;

cosθ = PQ/PB = x/9

In ΔPRA;

sinθ = PR/PA = y/3

Since, sin^{2} θ + cos^{2} θ = 1,

⇒ (y/3) + (x/9) = 1

⇒ x^{2}/81 + y^{2}/9 = 1

NCERT Solutions Class 11 Maths Chapter 11 Exercise ME Question 5

## 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

**Summary:**

The equation of the locus of point P on the rod is x^{2}/81 + y^{2}/9 = 1