Question

The line \( y - \sqrt{3}x + 3 = 0 \) cuts the parabola \( y^2 = x + 2 \) at the points \( P \) and \( Q \). If the coordinates of the point \( X \) are \( (\sqrt{3}, 0) \), then the value of \( XP \cdot XQ \) is:

• A. \( \frac{4(2+\sqrt{3})}{3} \)
• B. \( \frac{4(2-\sqrt{3})}{2} \)
• C. \( \frac{5(2+\sqrt{3})}{3} \)
• D. \( \frac{5(2-\sqrt{3})}{3} \)

Hint:

For product of distances: \begin{itemize} \item Use Vieta formulas. \item Convert distances into algebraic expressions. \end{itemize}

Answer 1

The Correct Option is A