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Find the length of latus rectum of the ellipse  \(\rm \frac{x^{2}}{16}= 1- \frac{y^{2}}{25}\) .

  1. \(\frac{16}{5}\)
  2. \(\frac{25}{2}\)
  3. \(\frac{32}{5}\)
  4. \(\frac{15}{2}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{32}{5}\)
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Detailed Solution

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Concept: 

quesImage6642 

Length of latus rectum of ellipse , L.R = \(\rm \frac{2a^{2}}{b}\)  [b > a] 

Calculation: 

The given equation are, \(\rm \frac{x^{2}}{16}= 1- \frac{y^{2}}{25}\)

⇒ \(\rm \frac{x^{2}}{16}+\frac{y^{2}}{25}=1\) 

On comparing with standard equation ,  a = 4 and b = 5 

As we know that , Length of latus rectum = \(\rm \frac{2a^{2}}{b}\) 

∴ L.R = \(\rm \frac{2\times16}{5}\) = \(\frac{32}{5}\) . 

The correct option is 3. 

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