text: Q
  
  # 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.
  
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  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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