AP EAMCET · Maths · Ellipse
Let the length of the latus rectum of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) be equal to the length of its semi-major axis. If the radius of its director circle is \(\sqrt{3}\) and \(\mathrm{e}\) is its eccentricity, then the length of its latus rectum is
- A \(\frac{1}{\mathrm{a}}\)
- B \(\frac{1}{b}\)
- C \(\frac{1}{\mathrm{e}}\)
- D \(\frac{1}{a b}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{\mathrm{e}}\)
Step-by-step Solution
Detailed explanation
Given equation of ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) Length of latus rectum \(=\frac{2 b^2}{a}=a\) \(\Rightarrow 2 b^2=a^2...(i)\) and equation of director circle is \(x^2+y^2=a^2+b^2 \Rightarrow x^2+y^2=3 b^2=(\sqrt{3} b)^2\) Since,…
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