Question
Download Solution PDFFind the length of latus rectum of the ellipse \(\rm \frac{x^{2}}{16}= 1- \frac{y^{2}}{25}\) .
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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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