AP EAMCET · Maths · Ellipse
Let \(x^2+y^2=20\) be the director circle of an ellipse \(E\) whose major axis is \(\mathrm{X}\)-axis and minor axis is \(\mathrm{Y}\)-axis. If the length of the latus rectum of \(\mathrm{E}\) is 2 , then the distance between its foci is
- A \(4 \sqrt{5}\)
- B \(4 \sqrt{3}\)
- C \(4 \sqrt{2}\)
- D 3
Answer & Solution
Correct Answer
(B) \(4 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
Equation of director circle ellipse is \[ x^2+y^2=a^2+b^2 \Rightarrow a^2+b^2=20 \] Given that lotus rectum \(=\frac{2 b^2}{a}=2 \Rightarrow b^2=a\) from (i) and (ii) we get \(a=4\) We have \(c^2=a^2-b^2=16-4=12\) \(\Rightarrow c=2 \sqrt{3}\) \(\therefore\) Distance between foci…
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