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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. - CBSE (Arts) Class 11 - Mathematics

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Question

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 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 [AB = 12 cm]

From P, draw PQ⊥OY and PR⊥OX

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Solution 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. Concept: Ellipse - Relationship Between Semi-major Axis, Semi-minor Axis and the Distance of the Focus from the Centre of the Ellipse.
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