Question:medium
The line \( y - \sqrt{3}x + 3 = 0 \) cuts the parabola \( y^2 = x + 2 \) at the points \( P \) and \( Q \). If the co-ordinates of the point \( X \) are \( (\sqrt{3}, 0) \), then the value of \( XP \cdot XQ \) is:
The line \( y - \sqrt{3}x + 3 = 0 \) cuts the parabola \( y^2 = x + 2 \) at the points \( P \) and \( Q \). If the co-ordinates of the point \( X \) are \( (\sqrt{3}, 0) \), then the value of \( XP \cdot XQ \) is:
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When dealing with distances between points and intersections of curves, forming a quadratic equation in one variable often simplifies the problem using Vieta's formulas.
Updated On: Nov 28, 2025
- \( \frac{4(2 + \sqrt{3})}{3} \)
- \( \frac{4(2 - \sqrt{3})}{2} \)
- \( \frac{5(2 + \sqrt{3})}{3} \)
- \( \frac{5(2 - \sqrt{3})}{3} \)
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