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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.

6.  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.

Views

Let $\theta$ be the angle that rod makes with the ground,

Now, at a point 3 cm from the end,

$\cos\theta=\frac{x}{9}$

At the point touching the ground

$\sin\theta=\frac{y}{3}$

Now, As we know the trigonometric identity,

$\sin^2\theta+\cos^2\theta=1$

$\left (\frac{x}{9} \right )^2+\left ( \frac{y}{3} \right )^2=1$

$\frac{x^2}{81}+\frac{y^2}{9}=1$

Hence the equation is,

$\frac{x^2}{81}+\frac{y^2}{9}=1$

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The text passage contains a mathematical question about determining the equation of the locus of a point on a moving rod, and it provides a detailed solution to this question.
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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.

6.  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.

Views

Let $\theta$ be the angle that rod makes with the ground,

Now, at a point 3 cm from the end,

$\cos\theta=\frac{x}{9}$

At the point touching the ground

$\sin\theta=\frac{y}{3}$

Now, As we know the trigonometric identity,

$\sin^2\theta+\cos^2\theta=1$

$\left (\frac{x}{9} \right )^2+\left ( \frac{y}{3} \right )^2=1$

$\frac{x^2}{81}+\frac{y^2}{9}=1$

Hence the equation is,

$\frac{x^2}{81}+\frac{y^2}{9}=1$

Exams
Articles
Questions
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The text passage contains a mathematical question about determining the equation of the locus of a point on a moving rod, and it provides a detailed solution to this question.

TYPE: SINGLE_QUESTION_WITH_ANSWER