JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let the length of the latus rectum of an ellipse with its major axis long \(x -\) axis and center at the origin, be \(8\). If the distance between the foci of this ellipse is equal to the length of the length of its minor axis, then which one of the following points lies on it?
- A \(\left( {4,\sqrt 2 ,2\sqrt 2 } \right)\)
- B \(\left( {4,\sqrt 3 ,2\sqrt 2 } \right)\)
- C \(\left( {4,\sqrt 3 ,2\sqrt 3 } \right)\)
- D \(\left( {4,\sqrt 2 ,2\sqrt 3 } \right)\)
Answer & Solution
Correct Answer
(B) \(\left( {4,\sqrt 3 ,2\sqrt 2 } \right)\)
Step-by-step Solution
Detailed explanation
Consider \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\) Given that \(2b = 2ae\) \( \Rightarrow b = ae\) and \(\frac{{2{b^2}}}{a} = 8\) \(a\left( {1 - {e^2}} \right) = 4,{a^2}{e^2} = {a^2}\left( {1 - {e^2}} \right)\) \( \Rightarrow {e^2} = \frac{1}{2}\)…
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