JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(S\) and \(S\,'\) be the foci of an ellipse and \(B\) be any one of the extremities of its minor axis. If \(\Delta S\,'BS\) is a right angled triangle with right angle at \(B\) and area \((\Delta S\,'BS) = 8\,sq.\) units, then the length of a latus rectum of the ellipse is
- A \(4\)
- B \(2\sqrt 2\)
- C \(4\sqrt 2\)
- D \(2\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\({m_{SB}}.{m_{S'B}} = 1\) \({b^2} = {a^2}{e^2}\,\,\,\,\,\,\,\,.......\left( i \right)\) \(\frac{1}{2}S'B.SB = 8\) \({a^2}{e^2} + {b^2} = 16\,\,\,\,\,\,\,\,.......\left( {ii} \right)\) \({b^2} = {a^2}\left( {1 - {e^2}\,} \right)\,\,\,\,\,\,\,\,.......\left( {iii} \right)\) using…
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