Find the latus rectum of the ellipse: $5 x^{2} + 4 y^{2} = 1$

\frac{2}{5}

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\frac{4}{5}

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\frac{8}{5}

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\frac{12}{5}

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Solution

The correct option is C $\frac{4}{5}$
$\frac{x^{2}}{{(\frac{1}{\sqrt{5}})}^{2}} + \frac{y^{2}}{{(\frac{1}{2})}^{2}} = 1$

Here, $a = \frac{1}{\sqrt{5}}, b = \frac{1}{2}$ and $a < b$

Now, $L R = \frac{2 a^{2}}{b} = \frac{4}{5}$
Ans: B

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