JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the distance between the foci of an ellipse is \(6\) and the distance between its directrices is \(12\), then the length of its latus rectum is
- A \(\sqrt 3\)
- B \(2\sqrt 3\)
- C \(3\sqrt 2\)
- D \(\frac{3}{\sqrt 2}\)
Answer & Solution
Correct Answer
(C) \(3\sqrt 2\)
Step-by-step Solution
Detailed explanation
Given \(2 \mathrm{ae}=6 \Rightarrow \quad \mathrm{ae}=3\dots(1)\) and \(\frac{2 a}{e}=12 \Rightarrow \mathbb{a}=6 e\dots(2)\) from \(( 1)\) and \(( 2)\) \(6 e^{2}=3 \Rightarrow \quad e=\frac{1}{\sqrt{2}}\) \(\Rightarrow \quad a=3 \sqrt{2}\) Now,…
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