AP EAMCET · Maths · Ellipse
If the latusrectum of an ellipse subtends a right angle at the centre of that ellipse, then the eccentricity of that ellipse is
- A \(\frac{\sqrt{5}+1}{4}\)
- B \(\frac{\sqrt{5}-1}{2}\)
- C \(\frac{\sqrt{10-2 \sqrt{5}}}{5}\)
- D \(\frac{\sqrt{10+2 \sqrt{5}}}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{\sqrt{5}-1}{2}\)
Step-by-step Solution
Detailed explanation
Let equation of ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) Let \(L L^{\prime}\) is latusrectum, then co-ordinate of \[ L\left(a e, \frac{b^2}{a}\right) \] \(L L^{\prime}\) subtend \(\pi / 2\) Angle at the centre, so angle \[ L C S=\pi / 4 \]…
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