JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
A hyperbola whose transverse axis is along the major axis of then conic, \(\frac{{{x^2}}}{3} + \frac{{{y^2}}}{4} = 4\) and has vertices at the foci of this conic . If the eccentricity of the hyperbola is \(\frac{3}{2}\) , then which of the following points does \(NOT\) lie on it ?
- A \(\left( {\sqrt 5 ,2\sqrt 2 } \right)\)
- B \((0, 2)\)
- C \(\left( {5,2\sqrt 3 } \right)\)
- D \(\left( {\sqrt 10 ,2\sqrt 3 } \right)\)
Answer & Solution
Correct Answer
(C) \(\left( {5,2\sqrt 3 } \right)\)
Step-by-step Solution
Detailed explanation
\(\left( c \right)\,\,\,\,\frac{{{x^2}}}{{12}} + \frac{{{y^2}}}{{16}} = 1\) \(e = \sqrt {1 - \frac{{12}}{{16}}} = \frac{1}{2}\) Foci \((0,2)\) &\((0,-2)\) So, transverse axis of hyperbola \(a = 2b = 4 \Rightarrow b = 2\) \({a^2} = {1^2}\left( {{e^2} - 1} \right)\)…
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