If the equations $x=1+2 \cos \theta, y=2+\sin \theta, 0 \leq \theta < 2 \pi$ represent an ellipse, then the point of intersection of the normal drawn at $\mathrm{P}\left(\frac{\pi}{4}\right)$ to this ellipse and its major axis is

• Correct answer
  A

  $\left(\frac{4-\sqrt{3}}{4}, 0\right)$
• B

  $\left(\frac{\sqrt{3}+1}{4}, 0\right)$
• C

  $\left(\frac{8+\sqrt{3}}{2}, 0\right)$
• D

  $\left(\frac{5}{2}, 0\right)$

Hence, the correct answer is option: 'A'.