JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
A hyperbola having the transverse axis of length \(\sqrt{2}\) has the same foci as that of the ellipse \(3 x^{2}+4 y^{2}=12,\) then this hyperbola does not pass through which of the following points?
- A \(\left(1,-\frac{1}{\sqrt{2}}\right)\)
- B \(\left(\sqrt{\frac{3}{2}}, \frac{1}{\sqrt{2}}\right)\)
- C \(\left(\frac{1}{\sqrt{2}}, 0\right)\)
- D \(\left(-\sqrt{\frac{3}{2}}, 1\right)\)
Answer & Solution
Correct Answer
(B) \(\left(\sqrt{\frac{3}{2}}, \frac{1}{\sqrt{2}}\right)\)
Step-by-step Solution
Detailed explanation
Ellipse \(: \frac{x^{2}}{4}+\frac{y^{2}}{3}=1\) eccentricity \(=\sqrt{1-\frac{3}{4}}=\frac{1}{2}\) \(\therefore\) foci \(=(\pm 1,0)\) for hyperbola, given \(2 a =\sqrt{2} \Rightarrow a =\frac{1}{\sqrt{2}}\) \(\therefore \quad\) hyperbola will be…
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