JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the point on the curve \(y^{2}=6 x\), nearest to the point \(\left(3, \frac{3}{2}\right)\) is \((\alpha, \beta)\), then \(2(\alpha+\beta)\) is equal to \(.....\)
- A \(3\)
- B \(9\)
- C \(12\)
- D \(27\)
Answer & Solution
Correct Answer
(B) \(9\)
Step-by-step Solution
Detailed explanation
Minimum distance is along the normal \(P \equiv\left(\frac{3}{2} \mathrm{t}^{2}, 3 \mathrm{t}\right)\) Normal at point \(\mathrm{P}\) \(t x+y=3 t+\frac{3}{2} t^{3}\) Passes through \(\left(3, \frac{3}{2}\right)\) \(\Rightarrow 3 t+\frac{3}{2}=3 t+\frac{3}{2} t^{3}\)…
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