AP EAMCET · Maths · Ellipse
Find the eccentricity of an ellipse, if the length of its latus rectum is 4 units and distance between its vertex and the nearest focus is \(3 / 2\) units.
- A \(\frac{1}{3}\)
- B \(\frac{2}{3}\)
- C \(\frac{1}{9}\)
- D \(\frac{3}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
Let the equation of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,(a > b)\) Then according to the question, Length of latus rectum \(=\frac{2 b^2}{a}=4\) ...(i) and \(\quad a-a e=\frac{3}{2} \Rightarrow a(1-e)=\frac{3}{2}\) ...(ii) From Eqs. (i) and (ii), we get…
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