JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
A helicopter is flying along the curve given by \(y - x^{3/2} = 7, (x \geq 0)\). A solider positioned at the point \(\left( {\frac{1}{2},7} \right)\) wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is
- A \(\frac{{\sqrt 5 }}{6}\)
- B \(\frac{1}{3}\sqrt {\frac{7}{3}} \)
- C \(\frac{1}{6}\sqrt {\frac{7}{3}} \)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{6}\sqrt {\frac{7}{3}} \)
Step-by-step Solution
Detailed explanation
\(y = {x^{3/2}} - 2\) \(\frac{{dy}}{{dx}} = \frac{3}{2}\sqrt x \) Slope of normal \( = - \frac{2}{{3\sqrt x }}\) Let point is \(\left( {{x_1},x_1^{3/2} - 2} \right)\) \(\therefore \) Normal…
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