TS EAMCET · Maths · Ellipse
If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8 , then the eccentricity is
- A \(\frac{1}{\sqrt{5}}\)
- B \(\frac{1}{2}\)
- C \(\frac{3}{5}\)
- D \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{5}\)
Step-by-step Solution
Detailed explanation
Here, \(2 a e=6\) and \(2 b=8 \Rightarrow b=4\) \(\begin{aligned} & b^2=16 \\ & \Rightarrow \quad a^2\left(1-e^2\right)=16 \\ & \Rightarrow \quad \frac{9}{e^2}\left(1-e^2\right)=16 \\ & \Rightarrow \quad 9-9 e^2=16 e^2 \\ & \Rightarrow \quad 25 e^2=9 \\ & \end{aligned}\)…
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