AP EAMCET · Maths · Ellipse
Let \(\mathrm{E}\) be an ellipse whose major axis is \(\mathrm{X}\)-axis and minor axis is \(\mathrm{Y}\)-axis. If the distance of a point \(\left(\frac{5}{2}, 2 \sqrt{3}\right)\) on \(\mathrm{E}\) from its foci are \(\frac{7}{2}\) and \(\frac{13}{2}\), then the eccentricity of the ellipse \(\mathrm{E}\) is
- A \(3 / 5\)
- B \(1 / 5\)
- C \(1 / \sqrt{5}\)
- D \(1 / \sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(3 / 5\)
Step-by-step Solution
Detailed explanation
Let the point \(\left(\frac{5}{2}, 2 \sqrt{3}\right)\) be \(\mathrm{P}\) Then, \(S P+S P=2 a\) \(\Rightarrow \frac{7}{2}+\frac{13}{2}=2 a \Rightarrow a=5\) The focus of the ellipse are \(( \pm a e, 0) \equiv( \pm 5 e, 0)\)…
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