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, sin² θ + cos² θ = 1,

⇒ (y/3) + (x/9) = 1

⇒ x²/81 + y²/9 = 1

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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 x²/81 + y²/9 = 1