JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the line \(y\, = \,mx\, + \,7\sqrt 3 \) is normal to the hyperbola \(\frac{{{x^2}}}{{24}} - \frac{{{y^2}}}{{18}} = 1,\) then a value of \(m\) is
- A \(\frac{2}{{\sqrt 5 }}\)
- B \(\frac{{\sqrt 5 }}{2}\)
- C \(\frac{{\sqrt {15} }}{2}\)
- D \(\frac{3}{{\sqrt 5 }}\)
Answer & Solution
Correct Answer
(A) \(\frac{2}{{\sqrt 5 }}\)
Step-by-step Solution
Detailed explanation
\(\frac{{{x^2}}}{{24}} - \frac{{{y^2}}}{{18}} = 1\,\,\,\,\, \Rightarrow a\, = \sqrt {24} :b\, = \sqrt {18} \) Paramentric normal: \(\sqrt {24} \cos \theta .x + \sqrt {18} .y\cot \theta = 42\) At \(x = 0;y = \frac{{42}}{{\sqrt {18} }}\tan \theta = 7\sqrt 3 \) (from given…
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