WBJEE · Maths · Parabola
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 \(X P \cdot X Q\) is
- A \(\frac{4(2+\sqrt{3})}{3}\)
- B \(\frac{4(2-\sqrt{3})}{2}\)
- C \(\frac{5(2+\sqrt{3})}{3}\)
- D \(\frac{5(2-\sqrt{3})}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{4(2+\sqrt{3})}{3}\)
Step-by-step Solution
Detailed explanation
Arbitrary point on the line \(\left(\sqrt{3}+\frac{r}{2}, \frac{r \sqrt{3}}{2}\right)\) satisfying in the parabola \(\Rightarrow 3 r^2-2 r-(4 \sqrt{3}+8)=0\) \(\because\) roots \(r_1\) & \(r_2\) \(\therefore\) product \(r_1 r_2=-\frac{4 \sqrt{3}+8}{3}\)…
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