Q117 / 170 · Manipal (MET) 2019 · Mathematics

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
    $\frac{1}{2}$
  • Correct answer
    C
    $\frac{3}{5}$
  • D
    $\frac{4}{5}$

Solution

$\begin{aligned} & \text { Here, } 2 a e=6 \text { and } 2 b=8 \Rightarrow b=4 \\ & \Rightarrow b^2=16 \Rightarrow a^2\left(1-e^2\right)=16 \\ & \Rightarrow \frac{9}{e^2}\left(1-e^2\right)=16 \Rightarrow 9-9 e^2=16 e^2 \\ & \Rightarrow \quad 25 e^2=9 \Rightarrow e=\frac{3}{5}\end{aligned}$

Hence, the correct answer is option: 'C'.

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