For the rectangular hyperbola xy - 36-find the value of Focal length-2eccentricity

Given, xy = c^2 ⇒ c = 6 Focal length of hyperbola nbsp; = 4c Focal length of hyperbola nbsp; =4×6 Focal length of hyperbola nbsp; =24 Eccentricity of th ...

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For the recta...

Question

For the rectangular hyperbola $x y = 36$ ,
find the value of $\frac{Focal length}{\sqrt{2} eccentricity}$

12.0

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Solution

Given,
$x y = c^{2} \Rightarrow c = 6$
$Focal length of hyperbola = 4 c Focal length of hyperbola = 4 \times 6 Focal length of hyperbola = 24$
$Eccentricity of the rectangular hyperbola = \sqrt{2}$
$∴ \frac{Focal length}{\sqrt{2} eccentricity} = \frac{24}{\sqrt{2} \times \sqrt{2}} = 12$

Suggest Corrections

For the rectangular hyperbola xy=36, find the value of Focal length√2eccentricity

Given, xy=c2⇒c=6 Focal length of hyperbola =4cFocal length of hyperbola =4×6Focal length of hyperbola =24 Eccentricity of the rectangular hyperbola =√2 ∴Focal length√2 eccentricity=24√2×√2=12

For the rectangular hyperbola $x y = 36$ ,
find the value of $\frac{Focal length}{\sqrt{2} eccentricity}$

Given,
$x y = c^{2} \Rightarrow c = 6$
$Focal length of hyperbola = 4 c Focal length of hyperbola = 4 \times 6 Focal length of hyperbola = 24$
$Eccentricity of the rectangular hyperbola = \sqrt{2}$
$∴ \frac{Focal length}{\sqrt{2} eccentricity} = \frac{24}{\sqrt{2} \times \sqrt{2}} = 12$