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Show that for rectangular hyperbola xy=c...

Show that for rectangular hyperbola `xy=c^2`

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Equation of given hyperbola is,
`xy= c^2`
It means vertices of hyperbola is `(c,c)` and `(-c,-c)`.
Focii will be `(sqrt2c,sqrt2c)` and `(-sqrt2c,-sqrt2c)`.
`:.` Length of transverse axis, `2a = sqrt((2c)^2+(2c)^2) = 2sqrt2c`
`=> a = sqrt2c`
Also, `(2c)^2 = a^2+b^2 => b^2 = 4c^2 - a^2`
`=>b^2 = 4c^2-(sqrt2c)^2=> b^2 = 2c^2 =>b = sqrt2c`
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